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Mathematical Study of the Nonlinear Partial Differential Equations Arising in the Statistical Mechanics

Research Project

Project/Area Number 16340047
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionOsaka University

Principal Investigator

SUZUKI Takashi  Osaka University, Graduate School of Engineering Science, Full Professor (40114516)

Co-Investigator(Kenkyū-buntansha) MATSUMURA Akitaka  Osaka University, Graduate School of Information Science, Full Professor (60115938)
ODANAKA Shinji  Osaka University, Cyber Media Center, Full Professor (20324858)
NAWA Hayato  Osaka University, Graduate School of Science, Full Professor (90218066)
WADA Takeshi  Kumamoto University, Faculty of Fngineering, Associate Professor (70294139)
NOBE Atsushi  Osaka University, Graduate School of Engineeriig Science, Assistant Professor (80397728)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥10,420,000 (Direct Cost: ¥10,000,000、Indirect Cost: ¥420,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2006: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2005: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2004: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywordsnonlinear problems / mean field hierarchy / blowup of the solution / variational structure / chemotaxis / self-interacting fluid / self-dual eauee theory / stationary turbulence / 非線形倫微分方程式 / 凝縮 / コラプス / 質量量子化 / 非平衡熱力学 / 自己重力流体 / 双対変分原理 / 平均場 / 爆発 / 臨界指数 / Trudinger-Moser不等式 / 非局所項 / 無限時間爆発 / 臨界現象 / スケーリング / 双対変分構造 / 力学系 / 圧縮性流体 / Gibbs測度 / 渦渡平均場方程式 / 対称化の方法 / 走化性方程式 / 自己相似解 / 界面 / Ginzburg-Landau理論
Research Abstract

In this research project, we provided a unified analysis to the critical phenomena, arising in the solution to the partial differential equation provided with the nonlinearity due to the self-interaction and the non-equilibrium. We formulate the mathematical principle across the hierarchy to control several phenomena common to many nonlinear problems. These problems are the mean field of stationary turbulence in high energy and of gauge field, Ricci flow, nonlinear parabolic equations, self-interacting fluids, material-energy transport, tumor growth, and nonlinear thermodynamics. Among them, we formulated the system of chemotaxis, derived in the context of th the formation of spores of the cellular slime molds, as the fundamental equation of the material transport subject to the mass conservation and the decrease of the free energy in the thermodynamics called Smoluchowski-Poisson equation and clarified the quantized blowup mechanism by developing various new methods of analysis. Then, we obtained the notions of the blowup envelope, formulation of the stationary and non-stationary states by the dual variation, hierarchical control of the stationary states upon the non-stationary states, which motivates the study on the structure and the stability of the set of stationary solutions of phenomenological equations concerning the critical phenomena arising in the non-equilibrium thermodynamics, formation of sub-collapses and the collision of collapses in the mean field equation arising in the gauge theory and turbulent theory and the semilinear parabolic equation with the critical Sobolev exponent, deformed quantization in the nonlinear parabolic equation with non-local term and the normalized Ricci flow, and mass quantization in higher dimensions.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (213 results)

All 2008 2007 2006 2005 2004 Other

All Journal Article (167 results) (of which Peer Reviewed: 66 results) Presentation (29 results) Book (15 results) Remarks (2 results)

  • [Journal Article] Variational and scaling properties of self-interacting fluids and their mass quantizations2008

    • Author(s)
      T. Suzuki
    • Journal Title

      Theoretical and Applied Mechanics Japan 56

      Pages: 207-213

    • NAID

      130004463629

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Derivation of the equilibrium mean field equations of point vortex system and Vortex filament system2008

    • Author(s)
      K. Sawada, et. al.
    • Journal Title

      Theoretical and Applied Mechanics Japan 56

      Pages: 285-290

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase field equation2008

    • Author(s)
      A.Ito, et. al.,
    • Journal Title

      Nonlinear Analysis 68

      Pages: 1825-1843

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Self-Similarity in Chemotaxis Systems2008

    • Author(s)
      T. Suzuki
    • Journal Title

      Colloquium Mathematics 111

      Pages: 11-34

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Ultradiscrete QRT maps and tropical elliptic curves2008

    • Author(s)
      A. Nobe
    • Journal Title

      J. Physics A: Mathematical and Theoretical 41

      Pages: 124-205

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Local property of the mountain-pass critical point and the mean field equation2008

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      Differential and Integral Equations 21

      Pages: 421-432

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Variational and scaling properties of self-interacting fluids and their mass quanti zations2008

    • Author(s)
      T., Suzuki
    • Journal Title

      Theoretical and Applied Mechanics Japan 56

      Pages: 207-213

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Derivation of the equilibrium mean field 'equations -of point vortex system and Vortex filament system2008

    • Author(s)
      K., Sawada, et. al.
    • Journal Title

      Theoretical and Applied Mechanics Japan 56

      Pages: 285-290

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase field equation2008

    • Author(s)
      A., Ito, et. al.
    • Journal Title

      Nonlinear Analysis 68

      Pages: 1825-1843

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Self-Similarity in chemotaxis systems2008

    • Author(s)
      T., Suzuki
    • Journal Title

      Colloquium Mathematics 111

      Pages: 11-34

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Ultradiscrete QRT- maps' and tropical elliptic curves2008

    • Author(s)
      A., Nobe
    • Journal Title

      J. Physics A : Mathematical and Theoretical 41

      Pages: 124-205

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Local property of the mountain-pass critical point and the mean field equation2008

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      Differential and Integral Equations 21

      Pages: 421-432

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Handbook of Differential Equations ; Stationary Partial Differential Equations,vol.52008

    • Author(s)
      T., Suzuki, et. al.
    • Journal Title

      Elsevier 93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase field equation2008

    • Author(s)
      A. Ito,.
    • Journal Title

      Nonlinear Analysis 68

      Pages: 1825-1843

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Derivation of the equilibrium mean field equations of point vortex system and Vortex filament system2008

    • Author(s)
      K. Sawada,.
    • Journal Title

      Theoretical and Applied Mechanics Japan 56

      Pages: 285-290

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mean field equation for equilibrium vortices with neutral orientation2007

    • Author(s)
      K. Sawada, et. al.
    • Journal Title

      Nonlinear Analysis 66

      Pages: 509-526

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Blowup analysis for $SU(3)$ Toda system2007

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      J. Differential Equations 232

      Pages: 419-440

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity2007

    • Author(s)
      Y. Naito, et. al.
    • Journal Title

      J. Differential Equations 232

      Pages: 176-211

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On the finite-time blowup of a parabolic equation describing chemotaxis2007

    • Author(s)
      N. Kavallaris, et. al.
    • Journal Title

      Differential and Integral Equations 20

      Pages: 293-308

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic non-degeneracy of the solution to the Liouville-Gel'fand problem in two dimensions2007

    • Author(s)
      T. Sato, et. al.
    • Journal Title

      Comment. Math. Helv. 82

      Pages: 353-369

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Stability of the steady state for the Falk model-system of shape memory alloys2007

    • Author(s)
      S. Yoshikawa, et. al.
    • Journal Title

      Math. Meth. Appl. Sci. 30

      Pages: 2233-2245

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Method of the blowup envelope and applications2007

    • Author(s)
      T. Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics 47-2

      Pages: 519-542

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Blowup in infinite time in the simplified system of chemotaxis.2007

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      Adv. Math. Sci. Appl. 17

      Pages: 445-472

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On a perturbed system of chemotaxis2007

    • Author(s)
      M. Kurokiba, et. al.
    • Journal Title

      International J. Mathematical Analysis 1

      Pages: 1261-1272

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Large-time behavior of solutions to an initial-boundary value problem on the half line for scalar viscous conservation law2007

    • Author(s)
      I. Hashimoto, et. al.
    • Journal Title

      Meth. Appl. Anal. 14

      Pages: 45-60

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Global existence and uniqueness of solutions to the Maxwell-Schroedinger equations2007

    • Author(s)
      M. Nakamura, et. al.
    • Journal Title

      Comm. Math. Phys. 276

      Pages: 315-339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Linearizable cellular automata2007

    • Author(s)
      A. Nobe, et. al.
    • Journal Title

      J. Physics A: Mathematical and Theoretical 40

      Pages: 7159-7174

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Mean field equation for equilibrium vortices with neutral orientation2007

    • Author(s)
      K., Sawada, et. al.
    • Journal Title

      Nonlinear Analysis 66

      Pages: 509-526

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Blowup analysis for $SU(3)$ Toda system2007

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      J. Differential Equations 232

      Pages: 419-440

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity2007

    • Author(s)
      Y., Naito, et. al.
    • Journal Title

      J. Differential Equations 232

      Pages: 176-211

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the finite-time blowup of a parabolic equation describing chemotaxis2007

    • Author(s)
      N., Kavallaris, et. al.
    • Journal Title

      Differential and Integral Equations 20

      Pages: 293-308

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic non-degeneracy of the solution to theLiouville-Gel'fand problem in two dimensions2007

    • Author(s)
      T., Sato, et. al.
    • Journal Title

      Comment. Math. Hely 82

      Pages: 353-369

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Stability of the steady state for the Falk model system of shape memory alloys2007

    • Author(s)
      S., Yoshikawa, et. al.
    • Journal Title

      Math. Meth. Appl. Sci 30

      Pages: 2233-2245

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Method of the blowup envelope and applications2007

    • Author(s)
      T., Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics 47-2

      Pages: 519-542

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Blowup in infinite time in the simplified system of chemotaxis2007

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      Adv. Math. Sci. Appl 17

      Pages: 445-472

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On a perturbed system of chemotaxis2007

    • Author(s)
      M., Kurokiba, et. al.
    • Journal Title

      International J. Mathematical Analysis 1

      Pages: 1261-1272

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Large-time behavior of solutions to an initial-boundary value problem on the half line for scalar viscous conservation law2007

    • Author(s)
      I., Hashimoto, et. al.
    • Journal Title

      Meth. Appl. Anal 14

      Pages: 45-60

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Global existence and uniqueness of solutions to the Maxwell-Schroedinger equations2007

    • Author(s)
      M., Nakamura, et. al.
    • Journal Title

      Comm. Math. Phys 276

      Pages: 315-339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Linearizable cellular automata2007

    • Author(s)
      A., Nobe, et. al.
    • Journal Title

      J. Physics A : Mathematical and Theoretical 40

      Pages: 7159-7174

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Mean field equation for equilibrium vortices with neutral orientation2007

    • Author(s)
      K. Sawada,.
    • Journal Title

      Nonlinear Analysis 66

      Pages: 509-526

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blowup analysis for $SU(3)$ Toda system2007

    • Author(s)
      H. Ohtsuka,.
    • Journal Title

      J. Differential Equations 232

      Pages: 419-440

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity.2007

    • Author(s)
      Y. Naito,.
    • Journal Title

      J. Differential Equations 232

      Pages: 176-211

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 0n the finite-time blowup of a parabolic equation describing chemotaxis2007

    • Author(s)
      N. Kavallaris,.
    • Journal Title

      Differential and Integral Equations 20

      Pages: 293-308

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic non-degeneracy of the solution to the Liouville-Gel'fand problem in two dimensions2007

    • Author(s)
      T. Sato,.
    • Journal Title

      Comment. Math. Helv. 82

      Pages: 353-369

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of the steady state for the Falk model system of shape memory alloys2007

    • Author(s)
      S. Yoshikawa,.
    • Journal Title

      Math. Meth. Appl. Sci. 30

      Pages: 2233-2245

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blowup in infinite time in the simplified system of chemotaxis2007

    • Author(s)
      H. Ohtsuka,.
    • Journal Title

      Adv. Math. Sci. Appl. 17

      Pages: 445-472

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 0n a perturbed system of chemotaxis2007

    • Author(s)
      M. Kurokiba,.
    • Journal Title

      International J. Mathematical Analysis 1

      Pages: 1261-1272

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blowup analysis for $SU(3)$ Toda system2007

    • Author(s)
      H.Ohtsuka, et al.
    • Journal Title

      J. Differential Equations 232

      Pages: 419-440

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity2007

    • Author(s)
      Y.Naito, et al.
    • Journal Title

      J. Differential Equations 232

      Pages: 176-211

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the finite-time blowup of a parabolic equation describing chemotaxis2007

    • Author(s)
      N.Kavallaris, et al.
    • Journal Title

      Differential and Integral Equations 20

      Pages: 293-308

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A blowup analysis to the mean field equation for arbitrarily-signed vortex2006

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      Banach Center Publications 74

      Pages: 185-197

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Interface vanishing for solutions to Maxwell and Stokes Systems2006

    • Author(s)
      T. Kobayashi, et. al.
    • Journal Title

      J. Mathematical Fluid Mechanics 8

      Pages: 382-397

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A quasi-linear parabolic system of chemotaxis2006

    • Author(s)
      T. Senba, et. al.
    • Journal Title

      Abstract and Applied Analysis

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Mean field equation for the equilibrium turbulence and a related functional inequality2006

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      Adv. Differential Equations 11

      Pages: 281-304

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The relaxation-time limit in the quantum hydrodynamic equations for semiconductors2006

    • Author(s)
      A. Juengel, et. al.
    • Journal Title

      J. Differential Equations 225

      Pages: 440-464

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Existence and stability of steady-state of one-dimensional quantum Euler-Poisson system for semi-conductors2006

    • Author(s)
      H. Li, et. al.
    • Journal Title

      J. Differential Equqations 225

      Pages: 1-25

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations2006

    • Author(s)
      F. Huang, et. al.
    • Journal Title

      Arch. Rational Mech. Anal. 179

      Pages: 55-77

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Soliton-antisoliton collision in the ultradiscrete modified KdV equation2006

    • Author(s)
      S. Isojima, et. al.
    • Journal Title

      Physics Letters A 357

      Pages: 31-35

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Ultradiscretization of elliptic functions and its applications to integrable systems2006

    • Author(s)
      A. Nobe
    • Journal Title

      J. Physics A: Mathematical and General 39

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems2006

    • Author(s)
      M. Murata, et. al.
    • Journal Title

      J. Physsics A: Mathematical and General 39

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A blowup analysis to the mean field equation for arbitrarily-signed vortex2006

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      Banach Center Publications 74

      Pages: 185-197

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Interface vanishing for solutions to Maxwell and Stokes Systems2006

    • Author(s)
      T., Kobayashi, et. al.
    • Journal Title

      J. Mathematical Fluid Mechanics 8

      Pages: 382-397

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A quasi-linear parabolic system of chemotaxis2006

    • Author(s)
      T., Senba, et. al.
    • Journal Title

      Abstract and Applied Analysis

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Mean field equation for the equilibrium turbulence and a related functional inequality2006

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      Adv. Differential Equations 11

      Pages: 281-304

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The relaxation-time limit in the quantum hydrodynamic equations for semiconductors2006

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    • Journal Title

      J, Differential Equations 225

      Pages: 440-464

    • Description
      「研究成果報告書概要(欧文)」より
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      2007 Final Research Report Summary
  • [Journal Article] Existence and stability of steady -state of one-dimensional quantum Euler-Poisson system for semi- conductors2006

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      H., Li, et. al.
    • Journal Title

      J. Differential Equqations 225

      Pages: 1-25

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations2006

    • Author(s)
      F., Huang, et. al.
    • Journal Title

      Arch. Rational Mech. Anal 179

      Pages: 55-77

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Soliton-antisoliton collision in the ultradiscrete modified KdV equation2006

    • Author(s)
      S., Isojima, et. al.
    • Journal Title

      Physics Letters A 357

      Pages: 31-35

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Ultradiscretization of elliptic functions and its applications to integrable systems2006

    • Author(s)
      A., Nobe
    • Journal Title

      J. Physics A : , Mathematical and General 39

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems2006

    • Author(s)
      M., Murata, et. al.
    • Journal Title

      J. Physics A : Mathematical and Generl 39

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Mean field equation for the equilibrium turbulence and a related functional inequality2006

    • Author(s)
      H.Ohtsuka, et al.
    • Journal Title

      Adv. Differential Equations 11

      Pages: 281-304

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      2006 Annual Research Report
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      Abstract and Applied Analysis

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      2006 Annual Research Report
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      J. Mathematical Fluid Mechanics 8

      Pages: 382-397

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      2006 Annual Research Report
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    • Author(s)
      H.Ohtsuka, et al.
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      Banach Center Publications 74

      Pages: 185-197

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    • Author(s)
      A.Ito, et al.
    • Journal Title

      Mathematical Approach to Nonlinear Phenomena : Modelling, Analysis and Simulation, edited by N. Kenmochi

      Pages: 129-146

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      2006 Annual Research Report
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    • Author(s)
      F.Huang, et al.
    • Journal Title

      Arch.Rational Mech.Anal. 179

      Pages: 55-77

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      2005 Annual Research Report
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    • Author(s)
      M.Nakamura, et al.
    • Journal Title

      Math.Ann. 332

      Pages: 565-604

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      2005 Annual Research Report
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    • Author(s)
      A. Kubo, et. al.
    • Journal Title

      Wseas Transactions on Biology and Biomedicine 2

      Pages: 45-50

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Some existence results for solutions to $SU(3)$ Toda system2005

    • Author(s)
      D. Chae, et. al.
    • Journal Title

      Calc. Vari. 24

      Pages: 403-429

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Finite element approximation for degenerate parabolic equations2005

    • Author(s)
      A. Mizutani, et. al.
    • Journal Title

      ESIAM: Mathematical Modelling and Numerical Analysis 39

      Pages: 755-780

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Inhomogeneous elliptic equation associated with critical Sobolev exponents2005

    • Author(s)
      K. Narukawa, et. al.
    • Journal Title

      Communications in Applied Analysis 9

      Pages: 505-525

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis2005

    • Author(s)
      N. Saito, et. al.
    • Journal Title

      Appl. Math. Comp. 171

      Pages: 72-90

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Convexity and uniqueness of the solution to the Liouville equation2005

    • Author(s)
      T. Sato, et. al.
    • Journal Title

      International J. Pure and Applied Mathematics 23

      Pages: 1-21

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Blow-up analysis for Liouville type equation in self-dual gauge field Theories2005

    • Author(s)
      H. Ohtsuka, et. al.
    • Journal Title

      Communications in Contemporary Analysis 7

      Pages: 177-205

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Sharp lower bound for the lifespan of systems of semilinear wave equations with multiple speeds2005

    • Author(s)
      S. Katayama, et. al.
    • Journal Title

      J. Math. Kyoto Univ. 45

      Pages: 391-403

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Local well-posedness for the Maxwell-Schrodinger equation2005

    • Author(s)
      N. Nakamura, et. al.
    • Journal Title

      Math. Ann. 332

      Pages: 565-604

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Periodic multiwave solutions to the Toda-type cellular automaton2005

    • Author(s)
      A. Nobe
    • Journal Title

      J. Physics A: Mathematical and General 38

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of the solution to Othmer-Stevens model2005

    • Author(s)
      A., Kubo, et. al.
    • Journal Title

      Wseas Transactions on Biology and Biomedicine 2

      Pages: 45-50

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Some existence results for solutions to $SU(3)$ Toda system2005

    • Author(s)
      D., Chae, et. al.
    • Journal Title

      Calc. Vari 24

      Pages: 403-429

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Finite element approximation for degenerate parabolic equations2005

    • Author(s)
      A., Mizutani, et. al.
    • Journal Title

      ESIAM : Mathematical Modelling and Numerical Analysis 39

      Pages: 755-780

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Inhomogeneous elliptic equation associated with critical Sobolev exponents2005

    • Author(s)
      K., Narukawa, et. al.
    • Journal Title

      Communications in Applied Analysis 9

      Pages: 505-525

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis2005

    • Author(s)
      N., Saito, et. al.
    • Journal Title

      Appl. Math. Comp 171

      Pages: 72-90

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Convexity and uniqueness of the solution to the.Liouville equation2005

    • Author(s)
      T., Sato, et. al.
    • Journal Title

      International J. Pure and Applied Mathematics 23

      Pages: 1-21

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Blow-up analysis for Lionville type quation in self-dual gauge field theories2005

    • Author(s)
      H., Ohtsuka, et. al.
    • Journal Title

      Communications in Contemporary Analysis 7

      Pages: 177-206

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Sharp lower bound for the Lifespan of systems of semilinear wave equations with multiple speeds2005

    • Author(s)
      S., Katayama, et. al.
    • Journal Title

      J. Math., Kyoto Univ 45

      Pages: 391-403

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Local well-posedness for the Maxwell-Schr\"odinger equation2005

    • Author(s)
      M., Nakamura, et. al.
    • Journal Title

      Math. Ann 332

      Pages: 565-604

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Periodic multiwave solutions to the Toda-type cellular automaton2005

    • Author(s)
      A., Nobe
    • Journal Title

      J. Physics A : Mathematical and General 38

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Free. Energy and Self-Interacting Particles2005

    • Author(s)
      T., Suzuki
    • Journal Title

      Birkhauser 359

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Blow-up analysis for Liouville type equation in self-dual gauge field theories2005

    • Author(s)
      H.Ohtsuka, et al.
    • Journal Title

      Communications in Contermporary Analysis 7

      Pages: 177-205

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      2005 Annual Research Report
  • [Journal Article] Convergence analysis of trial free boundary methods for the two-dimensional filtration problem2005

    • Author(s)
      T.Suzuki, et al.
    • Journal Title

      Numer.Math. 100

      Pages: 537-564

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      2005 Annual Research Report
  • [Journal Article] Convexity and uniqueness of the solution to the Liouville equation2005

    • Author(s)
      T.Sato, et al.
    • Journal Title

      International J.Pure and Applied Mathematics 23

      Pages: 1-21

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Inhomogeneous elliptic equation associated with critical Sobolev exponents2005

    • Author(s)
      K.Narukawa, et al.
    • Journal Title

      Communications in Applied Analysis 9

      Pages: 505-525

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      2005 Annual Research Report
  • [Journal Article] Finite element approximation for degenerate parabolic equations2005

    • Author(s)
      A.Mizutani, et al.
    • Journal Title

      ESIAM : Mathematical Modelling and Numerical Analysis 39

      Pages: 755-780

    • Related Report
      2005 Annual Research Report
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    • Author(s)
      Y.Matsuzawa, et al.
    • Journal Title

      Proceedings of the 5th East Asia PDE Conference (ed.H.J.Choe, C.-S.Lin, T.Suzuki, J.Wei)

      Pages: 179-204

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      2005 Annual Research Report
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    • Author(s)
      T.Kobayashi, et al.
    • Journal Title

      Proceedings of the 5th East Asia PDE Conference (ed.H.J.Choe, C.-S.Lin, T.Suzuki, J.Wei)

      Pages: 173-178

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      2005 Annual Research Report
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    • Author(s)
      T.Suzuki, et al.
    • Journal Title

      Resent Advances in Elliptic and Parabolic Problems (ed.C.-C.Chen, M.Chipot, C.-S.Lin)

      Pages: 259-270

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      2005 Annual Research Report
  • [Journal Article] Sharp lower bound for the lifespan of systems of semilinear wave equations with multiple speeds2005

    • Author(s)
      S.Katayama, et al.
    • Journal Title

      J.Math.Kyoto Univ. 45

      Pages: 391-403

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      2005 Annual Research Report
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    • Author(s)
      T.Wada
    • Journal Title

      Proceedings of the 5th East Asia PDE Conference (ed.H.J.Choe, C.-S.Lin, T.Suzuki, J.Wei)

      Pages: 319-328

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      2005 Annual Research Report
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    • Author(s)
      A.Kubo et al.
    • Journal Title

      Wseas Transactions on Biology and Biomedicine 1(2)

      Pages: 45-50

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      2004 Annual Research Report
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      土屋卓也 他
    • Journal Title

      応用数理 15(発表予定)

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      2004 Annual Research Report
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    • Author(s)
      A. Kubo, et. al.
    • Journal Title

      Differential and Integral Equations 17

      Pages: 721-736

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Non-local Gel'fand problem in higher dimension2004

    • Author(s)
      T. Miyasita, et. al.
    • Journal Title

      Banach Center Publications 66

      Pages: 221-235

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Non-topological condensates in self-dual Chern-Simons gauge theory2004

    • Author(s)
      T. Suzuki, et. al.
    • Journal Title

      Banach Center Publications 66

      Pages: 317-336

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Chemotactic collapse of radial solutions to J\"ager-Luckhaus system2004

    • Author(s)
      T. Senba, et. al.
    • Journal Title

      Adv. Math. Sci. Appl. 14

      Pages: 241-250

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Self-similar solutions-to a nonlinear parabolic-elliptic system2004

    • Author(s)
      Y. Naito, et. al.
    • Journal Title

      Taiwanise J. Math. 8

      Pages: 43-55

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Energy transport problem for self-gravitating particles2004

    • Author(s)
      T. Suzuki
    • Journal Title

      Taiwanise J. Math. 8

      Pages: 1-14

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary2004

    • Author(s)
      F. Huang, et. al.
    • Journal Title

      Osaka J. Math. 41

      Pages: 193-210

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Viscous shock wave to a gas-solid free boundary problem for compressible viscous gas2004

    • Author(s)
      F. Huang, et. al.
    • Journal Title

      SIAM J. Math. Anal. 36

      Pages: 498-522

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] An ultradiscretization of the sine-Gordon equation2004

    • Author(s)
      S. Isojima, et. al.
    • Journal Title

      Physics Letters A 331

      Pages: 378-386

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On reversibility of cellular automata with periodic boundary conditions2004

    • Author(s)
      A. Nobe, et. al.
    • Journal Title

      J.Physics A: Mathematical and General 37

      Pages: 5789-5804

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of the solution to a parabolic-ODE system modeling tumour growth2004

    • Author(s)
      A., Kubo, et. al.
    • Journal Title

      Differential and Integral Equations 17

      Pages: 721-736

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Non-local Gel'fand problem in higher dimension2004

    • Author(s)
      T., Miyasita, et. al.
    • Journal Title

      Banach Center Publications 66

      Pages: 221-235

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Non-topological condensates in self-dual Chern-Simons gauge theory2004

    • Author(s)
      T., Suzuki, et. al.
    • Journal Title

      Banach Center Publications 66

      Pages: 317-336

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Chemotactic collapse of radial solutions to Jager-Luckhaus system2004

    • Author(s)
      T., Senba, et. al.
    • Journal Title

      Adv. Math. Sci. Appl 14

      Pages: 241-250

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Self-similar solutions to a nonlinear parabolic - elliptic system2004

    • Author(s)
      Y., Naito, et. al.
    • Journal Title

      Taiwanise J. Math 8

      Pages: 43-55

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Energy transport problem for self-gravitating particles2004

    • Author(s)
      T., Suzuki
    • Journal Title

      Taiwanise J. Math 8

      Pages: 1-14

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the stability of contact discontinuity for compressible Navier-Stoke equations with free boundary2004

    • Author(s)
      F., Huang, et. al.
    • Journal Title

      Osaka J. Math 41

      Pages: 193-210

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Viscous shock wave to a gas-solid free boundary problem for compressible viscous gas2004

    • Author(s)
      F., Huang, et. al.
    • Journal Title

      SIAM J. Math. Anal 36

      Pages: 498-522

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] An ultradiscretization of the sine-Gordon equation2004

    • Author(s)
      S., Isojima, et. al.
    • Journal Title

      Physics Letters A 331

      Pages: 378-386

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On reversibility of cellular automata with periodic boundary conditions2004

    • Author(s)
      A., Nobe, et. al.
    • Journal Title

      J. Physics A : Mathematical and General 37

      Pages: 5789-5804

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Applied Analysis : Mathematical Methods in Natural Science2004

    • Author(s)
      T., Senba, et. al.
    • Journal Title

      Imperial College Press 378

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary2004

    • Author(s)
      F.Huang et al.
    • Journal Title

      Osaka J.Math. 41(1)

      Pages: 193-210

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On reversibility of cellular automata with periodic boundary condition2004

    • Author(s)
      A.Nobe et al.
    • Journal Title

      J.Phys.A : Mathematical and General 37

      Pages: 5789-5804

    • Related Report
      2004 Annual Research Report
  • [Journal Article] An ultradiscretization of the sine-Gordon equation2004

    • Author(s)
      S.Iojima et al.
    • Journal Title

      Physics Letters A 3312

      Pages: 378-336

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Energy transport problem for self-gravitating particles2004

    • Author(s)
      T.Suzuki
    • Journal Title

      Taiwanise J.Math. 8

      Pages: 1-14

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Self-similar solutions to a nonlinear parabolic-elliptic system2004

    • Author(s)
      Y.Naito et al.
    • Journal Title

      Taiwanise J.Math. 8

      Pages: 43-55

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Chemotactic collapse of radial solutions to Jager-Luckhaus system2004

    • Author(s)
      T.Senba et al.
    • Journal Title

      Adv.Math.Sci.Appl. 14

      Pages: 241-250

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Non-topological condensates in self-dual Chern-Simon gauge theory2004

    • Author(s)
      F.Takahashi et al.
    • Journal Title

      Banach Center Publications 66

      Pages: 317-336

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Non-local Gel' fand problem in higher dimension2004

    • Author(s)
      T.Miyasita et al.
    • Journal Title

      Banach Center Publications 66

      Pages: 221-235

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Asymptotic behavior of the solution to a parabolic-ODE system modeling chemotaxis2004

    • Author(s)
      A.Kubo et al.
    • Journal Title

      Differential and Integral Equations 17

      Pages: 721-736

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Weak solutions to the Navier-Stokes-Poisson equation

    • Author(s)
      T. Kobayashi, et. al.
    • Journal Title

      Adv. Math. Sci. Appl. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Touchdown and related problems in electrostatic MEMS device equation

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      N. Kavallaris, et. al.
    • Journal Title

      Nonlinear Differential Equations and Application. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Semilinear parabolic equation on bounded domain with critical Sobolev exponent

    • Author(s)
      T. Suzuki
    • Journal Title

      Indiana Univ. Math. J. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Capacity estimate for the blow-up set of parabolic equations

    • Author(s)
      F. Takahashi, et. al.
    • Journal Title

      Math. Z. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Weak solutions to the Navier-Stokes-Poisson equation

    • Author(s)
      T., Kobayashi, et. al.
    • Journal Title

      Adv. Math. Sci. Appl (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Touchdown and related Problems in electrostatic MEMS device equation

    • Author(s)
      N., Kavallaris, et. al.
    • Journal Title

      NDEA (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Semilinear parabolic equation on bounded domain with critical Sobolev exponent

    • Author(s)
      T., Suzuki
    • Journal Title

      Indiana Univ. Math. J (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Capacity estimate for the blow-up set of parabolic equations

    • Author(s)
      F., Takahashi, et. al.
    • Journal Title

      Math., Z (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Capacity estimate for the blow-up set of parabolic equations

    • Author(s)
      F. Takahashi,.
    • Journal Title

      Math. Z (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semilinear parabolic equation on bounded domain with critical Sobolev exponent

    • Author(s)
      T. Suzuki
    • Journal Title

      Indiana Univ. Math. J. (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Touchdown and related problems in electrostatic MEMS device equation

    • Author(s)
      N. Kavallaris,.
    • Journal Title

      Nonlinear Differential Equations and Applications. (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak solutions to the Navier-Stokes-Poisson equation.

    • Author(s)
      T. Kobayashi,.
    • Journal Title

      Adv Math. Sci. Appl. (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic non-degeneracy of the solution to the Liouville-Gel' fand problem in two dimensions

    • Author(s)
      T.Sato, et al.
    • Journal Title

      Commentarii Mathematici Helvetici (In press)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase field equation

    • Author(s)
      A.Ito, et al.
    • Journal Title

      Nonlinear Analysis (In press)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Method of the blowup envelope and applications

    • Author(s)
      T.Suzuki
    • Journal Title

      Asymptotic Analysis and Singularity (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Asymptotic non-degeneracy of the solution to the Liouville-Gel'fand problem in two dimensions

    • Author(s)
      T.Sato, et al.
    • Journal Title

      Commentarii Mathematici Helvetici (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Some existence results for solutions to $SU(3)$ Toda system

    • Author(s)
      D.Chae, et al.
    • Journal Title

      Calc.Vari. (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Interface vanishing for solutions to Maxwell and Stokes systems

    • Author(s)
      T.Kobayashi, et al.
    • Journal Title

      J.Mathematical Fluid Mechanics (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A quasi-linear parabolic system of chemotaxis

    • Author(s)
      T.Senba, et al.
    • Journal Title

      Abstract and Applied Analysis (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Mean field equation for the equilibrium turbulence and a related functional inequality

    • Author(s)
      H.Ohtsuka, et al.
    • Journal Title

      Adv.Differential Equations (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase field equation

    • Author(s)
      A.Ito, et al.
    • Journal Title

      Nonlinear Analysis (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Mean field equation for equilibrium vortices with neutral orientation

    • Author(s)
      K.Sawada, et al.
    • Journal Title

      Nonlinear Analysis (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Interface vanishing for solutions to Maxwell and Stokes systems

    • Author(s)
      T.Kobayashi et al.
    • Journal Title

      J. Mathematical Fluid Mechanics in Press

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Convergence analysis of trial free boundary methods for the two dimensional filtration problem

    • Author(s)
      T.Tsuchiya et al.
    • Journal Title

      Numer.Math. in Press

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some existence results for solutions to $SU(3)$ Toda system

    • Author(s)
      H.Ohtsuka et al.
    • Journal Title

      Calc.Vari. in Press

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Note on finite difference schemes to a parabolic-elliptic system modeling chemotaxis

    • Author(s)
      N.Saito et al.
    • Journal Title

      Appl.Math.Optim. in Press

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Parallel optimization applied to magnetoencephalography

    • Author(s)
      T.Suzuki
    • Journal Title

      J.Comp.Appl.Anal. in Press

    • Related Report
      2004 Annual Research Report
  • [Presentation] Analytic approach to the normalized Ricci flow2008

    • Author(s)
      鈴木貴
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Analytic approach to the normalized Ricci flow2008

    • Author(s)
      T. Suzuki
    • Organizer
      Calculus of variation applied to nonlinear PDE
    • Place of Presentation
      Hifa Institute of Technology
    • Year and Date
      2008-03-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Analytic approach to the normalized Ricci flow2008

    • Author(s)
      T., Suzuki
    • Organizer
      Calculus of Variation Applied to Nonlinear PDE
    • Place of Presentation
      Hifa Institute of Technology
    • Year and Date
      2008-03-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Analytic approach to the normalized Ricci flow2008

    • Author(s)
      T. Suzuki
    • Organizer
      Calculus of variation applied to nonlinear PDE
    • Place of Presentation
      Hifa Institute of Technology, Israel
    • Year and Date
      2008-03-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] 変分的双対性と非線形科学-オイラー生誕300年に寄せて2008

    • Author(s)
      鈴木貴
    • Organizer
      第43回Encounter with Mathematics, Euler300歳記念, 流体力学・変分学編, 始祖の業績と現在・未来への展開
    • Place of Presentation
      中央大学理工学部
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semilinear parabolic equation on bounded domain with critical Sobolev exponent2007

    • Author(s)
      T. Suzuki
    • Organizer
      Singularities Arising in Nonlinear Problems
    • Place of Presentation
      関西セミナーハウス
    • Year and Date
      2007-11-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semilinear parabolic equation on bounded domain with critical Sobolev exponent2007

    • Author(s)
      T. Suzuki
    • Organizer
      First Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDE
    • Place of Presentation
      Univ. Chile
    • Year and Date
      2007-10-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Semilinear parabolic equation on bounded domain with critical Sobolev exponent2007

    • Author(s)
      T. Suzuki
    • Organizer
      First Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDE
    • Place of Presentation
      Univ. Chile, Chile
    • Year and Date
      2007-10-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Global in time solution to a class of tumor growth systems2007

    • Author(s)
      鈴木貴
    • Organizer
      日本数学会総合分科会,
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semilinear parabolic equation on bounded domain with critical Sobolev exponent2007

    • Author(s)
      鈴木貴
    • Organizer
      日本数学会総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Capacity estimate for the blow-up set of parabolic equations2007

    • Author(s)
      鈴木貴
    • Organizer
      日本数学会総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semilinear parabolic equation on bounded domain with critical Sobolev exponent2007

    • Author(s)
      鈴木貴
    • Organizer
      変分問題とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-06-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic stability of a composite wave of two viscous shock waves for the equations of one-dimensional motion of the viscouand heat-2006

    • Author(s)
      A. Matsumura
    • Organizer
      Workshop on Mathematical Analysis on Nonlinear Phenomenain
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2006-12-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic stability of a composite wave of two viscous shock waves for the equations of one-dimensional motion of the viscous and heat-conductive gas2006

    • Author(s)
      A., Matsumura
    • Organizer
      Workshop on Mathematical Analysis on Nonlinear Phenomena
    • Place of Presentation
      Keio University
    • Year and Date
      2006-12-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Large time behavior of solutions of some one-dimensional models related to compressible fluids2006

    • Author(s)
      A. Matsumura
    • Organizer
      Applied Mathematics Seminar
    • Place of Presentation
      Chinese Academy of Science, Institute of Applied Mathematics
    • Year and Date
      2006-09-18
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Large time behavior of solutions of some one-dimensional models related to compressible fluids2006

    • Author(s)
      A., Matsumura
    • Organizer
      Applied Mathematics Seminar(Chinese Academy of Science, Institute of Applied Mathematics)
    • Year and Date
      2006-09-18
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Scaling and duality-some mathematical studies on the mean field Hierarchy2006

    • Author(s)
      T. Suzuki
    • Organizer
      The Sixth East Asia PDE Conference
    • Place of Presentation
      Wuhan University
    • Year and Date
      2006-05-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic behavior of solutions for a fluid dynamical model of semi-conductor equation2005

    • Author(s)
      A. Matsumura
    • Organizer
      Analysis Seminar, The Institute of Mathematical Sciences
    • Place of Presentation
      The Chinese University of Hong Kong
    • Year and Date
      2005-11-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic behavior of solutions for a fluid dynamical model of semi-conductor equation2005

    • Author(s)
      A., Matsumura
    • Organizer
      Analysis Seminar, The Institute of Mathematicatical Sciences
    • Place of Presentation
      The Chinese University of Hong Kong
    • Year and Date
      2005-11-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Large time behavior of solutions for one-dimensional compressible Navier-Stokes equations2005

    • Author(s)
      A. Matsumura
    • Organizer
      Hanoi Forum 2005
    • Place of Presentation
      Vietnam National University, Hanoi
    • Year and Date
      2005-09-28
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Large time behavior of solutions for one-dimensional compressible Navier-Stokes equations2005

    • Author(s)
      A., Matsumura
    • Organizer
      Hanoi Forum
    • Place of Presentation
      Vietnam National University, Hanoi
    • Year and Date
      2005-09-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Method of the blowup envelope and applications2005

    • Author(s)
      T. Suzuki
    • Organizer
      Self-Similar Solutions in Nonlinear PDE's
    • Place of Presentation
      Bedlevo
    • Year and Date
      2005-09-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] System of self-interacting particles-method of the blowup envelope2005

    • Author(s)
      T. Suzuki
    • Organizer
      Asymptotic Analysis and Singularity
    • Place of Presentation
      Sendai
    • Year and Date
      2005-07-26
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] System of self-interacting particles - method of the blowup envelope2005

    • Author(s)
      T., Suzuki
    • Organizer
      Asymptotic Analysis and Singularity
    • Place of Presentation
      Sendai
    • Year and Date
      2005-07-26
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic behavior and rate of blowup for solutions of the pseudo-conformally invariant nonlinear Schrodinger equation2005

    • Author(s)
      H. Nawa
    • Organizer
      The 5th East Asia PDE Conference
    • Place of Presentation
      大阪大学
    • Year and Date
      2005-02-01
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic behavior and rate of blowup for solutions of the pseudo' conformally invariant nonlinear Schrodinger equation2005

    • Author(s)
      H., Nawa
    • Organizer
      The 5th East Asia PDE Conference
    • Place of Presentation
      Osaka University
    • Year and Date
      2005-02-01
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic behavior of solutions for a fluid dynamical model of semiconductor equation2004

    • Author(s)
      A. Matumura
    • Organizer
      Colloquium, Department of Mathematics
    • Place of Presentation
      Capital Normal University, Beijing
    • Year and Date
      2004-10-28
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Mean field theories and dual variation2004

    • Author(s)
      T. Suzuki
    • Organizer
      Colloquim in honor of Professor D. Chae
    • Place of Presentation
      Sungkyunkwan University
    • Year and Date
      2004-04-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Mean field theories and dual variation2004

    • Author(s)
      T., Suzuki
    • Organizer
      Colloquim in honor of Professor'D. Chae
    • Place of Presentation
      Sungkyunkwan University
    • Year and Date
      2004-04-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Handbook of Differential Equations, Stationary Partial Differential Equations第5巻2008

    • Author(s)
      T. Suzuki, et. al.
    • Total Pages
      93
    • Publisher
      Elsevier
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Handbook of Differential Equations ; Stationary Partial Differential Equations,vol.52008

    • Author(s)
      T., Suzuki, et. al.
    • Total Pages
      93
    • Publisher
      Elsevier
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 数学の楽しみ, 逆問題の広がり2007

    • Author(s)
      鈴木貴, 他
    • Total Pages
      144
    • Publisher
      日本評論社
    • Related Report
      2007 Annual Research Report
  • [Book] Free Energy and Self-Interacting Particles2005

    • Author(s)
      T. Suzuki
    • Total Pages
      359
    • Publisher
      Birkh\"auser
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Free. Energy and Self-Interacting Particles2005

    • Author(s)
      T., Suzuki
    • Total Pages
      359
    • Publisher
      Birkhauser
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 偏微分方程式講義-半線形楕円型方程式の理論2005

    • Author(s)
      上岡有紀, 鈴木貴
    • Total Pages
      170
    • Publisher
      培風館
    • Related Report
      2005 Annual Research Report
  • [Book] Free Energy and Self-Interacting Particles2005

    • Author(s)
      T.Suzuki
    • Total Pages
      359
    • Publisher
      Birkhauser
    • Related Report
      2005 Annual Research Report
  • [Book] Free Energy and Self-Interacting Particles2005

    • Author(s)
      T.Suzuki
    • Total Pages
      366
    • Publisher
      Birkh" auser
    • Related Report
      2004 Annual Research Report
  • [Book] Applied Analysis: Mathematical Methods in Natural Science2004

    • Author(s)
      T. Senba, et. al.
    • Total Pages
      378
    • Publisher
      Imperial College Press
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Applied Analysis : Mathematical Methods in Natural Science2004

    • Author(s)
      T., Senba, et. al.
    • Total Pages
      378
    • Publisher
      Imperial College Press
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 非線形微分方程式の大域解-圧縮性流体の数学解析2004

    • Author(s)
      松村昭孝 他
    • Total Pages
      303
    • Publisher
      日本評論社
    • Related Report
      2004 Annual Research Report
  • [Book] Applied Analysis : Mathematical Methods in Natural Science2004

    • Author(s)
      T.Senba et al.
    • Total Pages
      378
    • Publisher
      Imperial College Press
    • Related Report
      2004 Annual Research Report
  • [Book] Handbook of Differential Equations, Stationary Partial Differential Equations第5巻

    • Author(s)
      F. Takahashi,.
    • Publisher
      Elsevier, Amsterdam.(印刷中)
    • Related Report
      2007 Annual Research Report
  • [Book] 応用解析学ハンドブック, 楕円型方程式

    • Author(s)
      増田久弥(編), 他
    • Publisher
      東京スプリンガー(印刷中)
    • Related Report
      2007 Annual Research Report
  • [Book] 自己組織化ハンドブック, 血管新生

    • Author(s)
      国武豊喜(編), 他
    • Publisher
      エヌ・ティー・エス(印刷中)
    • Related Report
      2007 Annual Research Report
  • [Remarks] 「研究成果報告書概要(和文)」より

    • URL

      http://www.sigmath.es.Osaka-u.ac.jp/suzuki/index.html

    • Related Report
      2007 Final Research Report Summary
  • [Remarks]

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/suzuki/index.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

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