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2006 Fiscal Year Final Research Report Summary

Research on global solutions in time and their asymptotic behaviors for viscous and relaxation models of conservation laws

Research Project

Project/Area Number 15340043
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MATSUMURA Akitaka  Osaka University, Graduate School of Information Science and Technology, Professor, 大学院情報科学研究科, 教授 (60115938)

Co-Investigator(Kenkyū-buntansha) HAYASHI Nakao  Osaka University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (30173016)
KOTANI Shin'ichi  Osaka University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (10025463)
ODANAKA Shinji  Osaka University, Cybermedia Center, Professor, サイバーメディアセンター, 教授 (20324858)
NISHIHARA Kenji  Waseda University, Dept.of Politics and Economics, Professor, 政治経済学部, 教授 (60141876)
NISHIBATA Shinya  Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Associate Professor, 大学院情報理工学研究科, 助教授 (80279299)
Project Period (FY) 2003 – 2006
Keywordsconservation law / asymptotic stability / boundary layer / viscous shock wave / viscous contact wave / semiconductor / quantum fluid. dynamical model / dissipative wave equation
Research Abstract

1.Initial boundary value problems on the half space to one-dimensional isentropic models for compressible fluid are investigated. In a case where the fluid inflows on the boundary, it is proved that the superposition of the boundary layer solution and viscous shock wave (or rarefaction wave) is asymptotically stable under some smallness conditions. In a case where the fluid outflows on the boundary, the existence of the boundary layer solution and its asymptotic stability are also proved. Furthermore, an initial boundary value problem on the half space to a one-dimensional ideal gas model (3 by 3 system) is investigated, and then the asymptotic stability of the viscous contact wave is proved. The asymptotic stability of the viscous contact wave for the Cauchy problem is also proved, if the integral of the initial perturbation is zero. Among multi-dimensional problems, it is proved that the spherically symmetric solution of an isothermal model of the compressible Navier-Stokes equation … More globally exists in time and tends toward its stationary solution.
2.Initial boundary value problems for a one-dimensional model which describes the movement of electrons in semiconductors are investigated. It is proved that even for any large doping profile the stationary solution exits and is asymptotically stable. As for the multi-dimensional models, an iterative algorithm of numerical computation with high resolution to simulate the stationary solutions is developed.
3.Asymptotic behavior of solutions of a one-dimensional model of compressible viscous fluid in porous media is investigated. It is proved that the solution tends toward a diffusion wave of a parabolic equation, and the precise decay rate of asymptotics to the diffusion wave is also obtained.
4.Asymptotic behavior of solutions of nonlinear dispersive equations and dissipative equations with a critical nonlinearity is investigated. It is proved that the solution of dissipative wave equation tends toward a self-similar solution of a heat equation. As for the dispersive equations, a new result on how the resonance phenomena between the characteristic frequency number of the linearized equation and that of nonlinear term influences the asymptotic behavior of the solutions. Less

  • Research Products

    (20 results)

All 2007 2006 2004 2003 Other

All Journal Article (19 results) Book (1 results)

  • [Journal Article] Asymptotic stability of a stationary solution to a hydrodynamic model for semiconductors2007

    • Author(s)
      S.Nishibata, M.Suzuki
    • Journal Title

      Osaka Journal of Mathematics (to appear)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A high-resolution method for quantum confinement transport simulations in MOSFETs2007

    • Author(s)
      S.Odanaka
    • Journal Title

      IEEE Transactions on CAD of ICAS 26

      Pages: 80-85

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

    • Author(s)
      F.Huang, A.Matsumura, Z.Xin
    • Journal Title

      Archive for Rational Mechanics and Analysis 179

      Pages: 55-77

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Existence and stability of steady-state of one-dimensional quantum Euler-Poisson system for semiconductors2006

    • Author(s)
      H.Li, F.Huang, A.Matsumura
    • Journal Title

      J. Differential Equations 225

      Pages: 1-25

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Global asymptotics for the damped wave equation with absorption in higher dimensional space2006

    • Author(s)
      K.Nishihara
    • Journal Title

      J. Math. Soc. Japan 58

      Pages: 805-836

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Domain and range of the modified wave operator for Schroedinger equations with a critical nonlinearity2006

    • Author(s)
      N.Hayashi, P.I.Naumkin
    • Journal Title

      Commun. Math. Phys. 267

      Pages: 477-492

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Existence and stability of steady-state of one-dimensional quantum Euler-Poisson system for semiconductors2006

    • Author(s)
      H.Li, F.Huang, A.Matsumura
    • Journal Title

      J.Differential Equations 225

      Pages: 1-25

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Global asymptotics for the damped wave equation with absorption in higher dimensional space2006

    • Author(s)
      K.Nishihara
    • Journal Title

      J.Math.Soc.Japan 58

      Pages: 805-836

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Domain and range of the modified wave operator for Schroedinger equations with a critical nonlinearity2006

    • Author(s)
      N.Hayashi, P.I.Naumkin
    • Journal Title

      Commun.Math.Phys.

      Pages: 477-492

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

    • Author(s)
      F.Huang, A.Matsumura, X.Shi
    • Journal Title

      SIAM J. Math. Anal. 36

      Pages: 498-522

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Large-time behavior of spherically symmetric solutions to an isentropic model of compressible viscous fluid in a field of potential forces2004

    • Author(s)
      T.Nakamura, S.Nishibata, S.Yanagi
    • Journal Title

      Math. Models and Methods Appl. Sci. 14

      Pages: 1849-1879

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Multidimensional discretization of the stationary quantum drift-diffusion model for ultra-small MOSFET structures2004

    • Author(s)
      S.Odanaka
    • Journal Title

      IEEE Transactions on CAD of ICAS 23

      Pages: 837-842

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

    • Author(s)
      F.Huang, A.Matsumura, X.Shi
    • Journal Title

      SIAM J.Math.Anal. 36

      Pages: 498-522

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Multidimensional discretization of the stationary quantum drift-diffusion model for ultra-small MOSFET structures2004

    • Author(s)
      S.Odanaka
    • Journal Title

      IEEE Transactions on CAD of ICAS 223

      Pages: 837-842

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Viscous shock wave and boundary layer solution to an inflow problem2003

    • Author(s)
      F.Huang, A.Matsumura, X.Shi
    • Journal Title

      Commun. Math. Phys. 239

      Pages: 261-285

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media2003

    • Author(s)
      K.Nishihara
    • Journal Title

      Proc. Roy. Soc. Edinburgh, Sect. A 133

      Pages: 177-196

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Viscous shock wave and boundary layer solution to an inflow problem2003

    • Author(s)
      F.Huang, A.Matsumura, X.Shi
    • Journal Title

      Commun.Math.Phys. 239

      Pages: 261-285

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media2003

    • Author(s)
      K.Nishihara
    • Journal Title

      Proc.Roy.Soc.Edinburgh, Sect.A 133

      Pages: 177-196

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotic stability of a stationary solution to a hydrodynamic model for semiconductors

    • Author(s)
      S.Nishibata, M.Suzuki
    • Journal Title

      Accepted and to appear in Osaka Journal of Mathematics

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] 非線形微分方程式の大域解,圧縮性粘性流の数学解析2004

    • Author(s)
      松村昭孝, 西原健二
    • Total Pages
      303
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2008-05-27  

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