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Mathematical Models of Interfacial Motion of Crystalline Materials

Research Project

Project/Area Number 16340021
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHiroshima University

Principal Investigator

KOBAYASHI Ryo  Hiroshima University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (60153657)

Co-Investigator(Kenkyū-buntansha) GIGA Yoshikazu  Tokyo University, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (70144110)
NAGAYAMA Masaharu  Kanazawa University, Graduate School of Natural Science, Associate Professor, 大学院自然科学研究科, 助教授 (20314289)
NONOMURA Makiko  Hiroshima University, Graduate School of Science, Assistant, 大学院理学研究科, 助手 (20333320)
MIMURA Masayasu  Meiji University, Fuculty of Science and Technology, Professor, 理工学部, 教授 (50068128)
UEYAMA Daishin  Meiji University, Fuculty of Science and Technology, Lecturer, 理工学部, 講師 (20304389)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥12,500,000 (Direct Cost: ¥12,500,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2005: ¥5,500,000 (Direct Cost: ¥5,500,000)
Fiscal Year 2004: ¥5,700,000 (Direct Cost: ¥5,700,000)
Keywordspolycrystal / phase field / singular diffusivity / manifold-valued function / rotation group / grain boundary / 等長埋め込み / フェーズフィールドモデル / SO(3) / ドメイン成長 / 数理モデル
Research Abstract

Kobayashi had benn investigated the problem for the mathematical model of grain boundary in polycrystalline materials since the middle of 90's, and completed 2D model already. The main goal of this research is to extend Kobayashi-Warren-Carter model to 3D model, which includes essential difficulties because the orientation variable must be extended from SO(2)-valued to SO(3)-valued. Therefore we intended to formuLate the 3D model mathematically, study mathematical theories concerning to it, ・and develop the technique of numerical simulation.
We first construct the SO(3)-valued singular diffusivity equation in one dimensional and two dimensional space, and simulation codes. Then we compare the 2 expressions for SO(3); local coordinates (Rodrigues, Vector) and imbedding to 9 dimensional Euclidean space R^{9}, and concluded that the imbedding method is the way we have to go. According to this decision we first developed a 3D numerial code in which the values of orientation variables are kept in SO(3) by means of the normal projection to SO(3) and some special penalty, function. By coupling this orientation equation with the phase field equation which describes the solid-liquid phase dynamics, we completed the model and 3D numerical code which can describe the while process from nucleation, solidification, formation of grain boundaries and growth of the grains accompanied by the motion of grain boundaries.
Finally in order to include the symmetries of crystalline structure to our model, we took the orientation space as the homogeneous space (the space obtained by dividing SO(3) by symmetry group) and tried to imbed.it to some (higher dimensional) Euclidian space. However we found it is very difficult to obtain the concrete imbedding in the situation where we are interested in.
Our research has interesting side effect, which is a construction of mathematical model of cleavage which can be considered (in some sense) to be a reverse process of coarsening of grains.

Report

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

    (94 results)

All 2006 2005 2004 Other

All Journal Article (92 results) Book (2 results)

  • [Journal Article] Physarum solver : -a biologically inspired method of road-network navigation2006

    • Author(s)
      A.Tero
    • Journal Title

      Physica A 363

      Pages: 115-119

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Mathematical model for rhythmic protoplasmic movement in the true slime mold2006

    • Author(s)
      R.Kobayashi
    • Journal Title

      J. Math. Biol. 53

      Pages: 273-286

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Fddd strueture in AB-type-diblock copolymers2006

    • Author(s)
      K.Yamada
    • Journal Title

      J. Phys. : Condens. Matter 18

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] マランゴニ対流の2次元モデルで見られるパターンとダイナミクス2006

    • Author(s)
      野々村真規子
    • Journal Title

      応用数理 16

      Pages: 20-30

    • NAID

      110004833281

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Interacting Spots in Reaction-Diffusion Systems2006

    • Author(s)
      S.-I.Ei
    • Journal Title

      J. Disc.Cont. Dynamical Systems, Ser. A 14

      Pages: 31-62

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Fast reaction limits and Liesegang bands2006

    • Author(s)
      D.Hilhorst
    • Journal Title

      Inter. Series of Numerical Math. 154

      Pages: 241-250

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Traveling front solutions in a chemotaxis-growth model2006

    • Author(s)
      M.Funaki
    • Journal Title

      J. Free Boundaries and Interfaces 8

      Pages: 223-245

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Selfsimilar expanding solutions in a sector for a crystalline flow2006

    • Author(s)
      M.-H.Giga, Y.Giga, H.Hontani
    • Journal Title

      SIAM J. Math. Anal 37

      Pages: 1207-1226

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Navier-Stokes equations in a rotating frame in $ {bfR}^3$ with initial data nondecreasing at infinity2006

    • Author(s)
      Y.Giga, K.Inui, A.Mahalov, S.Matsui
    • Journal Title

      Hokkaido Math. J. 35

      Pages: 321-364

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability of facets of crystals from vapor2006

    • Author(s)
      Y.Giga, P.Rybka
    • Journal Title

      Discrete Contin Dyn. Syst 14

      Pages: 689-706

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations2006

    • Author(s)
      Y.Giga, T.Ohtsuka, R.Schatzle
    • Journal Title

      Interfaces and Free Boundaries 8

      Pages: 317-348

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global solvability of constrained singular diffusion equation associated with essential variation2006

    • Author(s)
      Y.Giga, H.Kuroda, N.Yamazaki
    • Journal Title

      Proc. Free boundary problem 2005, Internationalseries of Namerical Math 154

      Pages: 209-218

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On blow up at space infinity for semilinear heat equations2006

    • Author(s)
      Y.Giga, N.Umeda
    • Journal Title

      J. Math. Anal. Appl 316

      Pages: 538-555

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Physarum solver : -a biologically inspired method of road-network navigation-2006

    • Author(s)
      A.Tero, R.Kobayashi, T.Nakagaki
    • Journal Title

      Physica A 363

      Pages: 115-119

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Mathematical model for rhythmic protoplasmic movement in the true slime mold2006

    • Author(s)
      R.Kobayashi, A.Tero, T.Nakagaki
    • Journal Title

      J. Math. Biol. 53

      Pages: 273-286

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability of facets of crystals from vapor2006

    • Author(s)
      Y.Giga, P.Rybka
    • Journal Title

      Discrete Contin. Dyn. Syst 14

      Pages: 689-706

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations2006

    • Author(s)
      Y.Giga, T.Ohtsuka, R.Shatzle
    • Journal Title

      Interfaces and Free Boundaries 8

      Pages: 317-348

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Fddd structure in AB-type diblock copolymers2006

    • Author(s)
      K.Yamada, M.Nonomura, T.Ohta
    • Journal Title

      J. Phys. : Condens. Matter 18

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Interacting Spots in Reaction-Diffusion Systems2006

    • Author(s)
      S.-I.Ei, M.Mimura, M.Nagayama
    • Journal Title

      J. Discrete and Continuous Dynamical Systems, Series A 14

      Pages: 31-62

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Traveling front solutions in a chemotaxis-growth model2006

    • Author(s)
      M.Funaki, M.Mimura, A.Tsujikawa
    • Journal Title

      J. Free Boundaries and Interfaces 8

      Pages: 223-245

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Diffusion, Cross-diffusion and Competitive Interaction2006

    • Author(s)
      M.Iida, M.Mimura, H.Ninomiya
    • Journal Title

      J. Math. Biol. 53

      Pages: 617-641

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Fast reaction limits and Liesegang bands2006

    • Author(s)
      D.Hilhorst, R.van der Hout, M.Mimura, I.Ohnishi
    • Journal Title

      Inter. Series of Numerical Math. 154

      Pages: 241-250

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Lower estimate of attractor dimension for chemotaxis-growth system2006

    • Author(s)
      M.Aida, T.Tsujikawa, M.Efendiev, A.Yagi, M.Mimura
    • Journal Title

      J. London Math. Soc. 74

      Pages: 453-474

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Selfsimilar expanding solutions in a sector for a crystalline flow2006

    • Author(s)
      M.-H.Giga
    • Journal Title

      SIAM J. Math. Anal 37

      Pages: 1207-1226

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of facets of crystals from vapor2006

    • Author(s)
      Y.Giga
    • Journal Title

      Discrete Contin. Dyn. Syst 14

      Pages: 689-706

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations2006

    • Author(s)
      Y.Giga
    • Journal Title

      Interfaces and Free Boundaries 8

      Pages: 317-348

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Fddd structure in AB-type diblock copolymers2006

    • Author(s)
      K.Yamada
    • Journal Title

      J.Phys. : Condens.Matter 18

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Traveling front solutions in a chemotaxis-growth model2006

    • Author(s)
      M.Funaki
    • Journal Title

      J. Free Boundaries Interfaces 8

      Pages: 223-245

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Interacting spots in reaction-diffusion systems2006

    • Author(s)
      S.-I.Ei
    • Journal Title

      Disc.Cont.Dynamical Systems, Ser.A 14

      Pages: 31-62

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of-plasmodial slime molds2005

    • Author(s)
      A.Tero
    • Journal Title

      Physica D 205

      Pages: 125-135

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Collective movement of epithelial cells on a collagen gel substrate2005

    • Author(s)
      H.Haga
    • Journal Title

      Biophysical Journal 88

      Pages: 1-7

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Modeling the formation and dynamics of polycrystals in 3D2005

    • Author(s)
      R.Kobayashi
    • Journal Title

      Physica A 356

      Pages: 127-132

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] Signal propagation and failure in one-dimensional FitzHugh-Nagumo equations with periodic stimuli2005

    • Author(s)
      T.Yanagita
    • Journal Title

      Phys. Rev. E 036226

      Pages: 1-4

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis2005

    • Author(s)
      H.Hontani, M.-H.Giga, Y.Giga, K.Deguchi
    • Journal Title

      Discrete Appl. Math 147

      Pages: 265-285

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability of facets of self-similar motion of a crystal2005

    • Author(s)
      Y.Giga, P.Rybka
    • Journal Title

      Adv. Differential Equations 10

      Pages: 601-634

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations2005

    • Author(s)
      Y.Giga, M.Ohnuma
    • Journal Title

      Int. J. Pure Appl. Math. 22

      Pages: 165-184

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Uniform local solvabilty for the Navier-Stokes equations with the Coriolis force2005

    • Author(s)
      Y.Giga, K.Inui, A.Mahalov, S.Matsui
    • Journal Title

      Methods Appl. Anal 12

      Pages: 381-393

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Blow-up directions at space infinity for solutions of semilinear heat equations2005

    • Author(s)
      Y.Giga, N.Umeda
    • Journal Title

      Bol. Soc. Paran. Mat (3) 23

      Pages: 9-28

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On singular vertical diffusion for some Hamilton-Jacobi equations2005

    • Author(s)
      M.-H.Giga, Y.Giga
    • Journal Title

      Viscosity solution theory of differential equations and its developments, RIMS

      Pages: 131-141

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A characterization of value functions by viscosity solutions(粘性解による値関数の特徴づけ)2005

    • Author(s)
      Y.Giga, S.Koike
    • Journal Title

      ISCIE 49

      Pages: 2-7

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chemo-Sensitive Running Droplet2005

    • Author(s)
      Y.Sumino
    • Journal Title

      Physical Review E 72

      Pages: 41603-41603

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Interacting spots in reaction diffusion systems2005

    • Author(s)
      K.Yamada
    • Journal Title

      J. Phys. : Condens. Matter 17

      Pages: 4877-4887

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Micro-phase separation in rod-coil copolymers2005

    • Author(s)
      T.Ohta
    • Journal Title

      J. Phys. : Condens. Matter 17

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chemotaxis and growth system with singular sensitivity function2005

    • Author(s)
      M.Aida
    • Journal Title

      Nonlinear Anal. 6

      Pages: 323-336

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chaotic Pulses for Discrete Reaction Diffusion Systems2005

    • Author(s)
      Y.Nishiura
    • Journal Title

      SIADS 4

      Pages: 733-754

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds2005

    • Author(s)
      A.Tero, R.Kobayashi, T.Nakagaki
    • Journal Title

      Physica D 205

      Pages: 125-135

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Collective movement of epithelial cells on a collagen gel substrate2005

    • Author(s)
      H.Haga, C.Irahara, R.Kobayashi, T.Nakagaki, K.Kawabata
    • Journal Title

      Biophysical Journal 88

      Pages: 1-7

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Modeling the formation and dynamics of polycrystals in 3D2005

    • Author(s)
      R.Kobayashi, J.A.Warren
    • Journal Title

      Physica A 356

      Pages: 127-132

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Signal propagation and failure in one-dimensional FitzHugh-Nagumo equations with periodic stimuli2005

    • Author(s)
      T.Yanagita, Y.Nishiura, R.Kobayashi
    • Journal Title

      Phys. Rev. E 036226

      Pages: 1-4

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability of facets of self-similar motion of a crystal2005

    • Author(s)
      Y Gigaand P.Rybka
    • Journal Title

      Adv. Differential Equations 10

      Pages: 601-634

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations2005

    • Author(s)
      Y.Giga, M.Ohnuma
    • Journal Title

      Int. J. Pure Appl.Math 22

      Pages: 165-184

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Uniform local solvability for the Navier-Stokes equations with the Coriolis force2005

    • Author(s)
      Y.Giga, K.Inui, A.Mahalov, S.Matsui
    • Journal Title

      Methods Appl. Anal. 12

      Pages: 381-393

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A characterization of value functions by viscosity solutions2005

    • Author(s)
      Y.Giga, S.Koike
    • Journal Title

      ISCIE 49

      Pages: 2-7

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chemo-Sensitive Running Droplet2005

    • Author(s)
      Y.Sumino, M.Nagayama, H.Kitahata, S.M.Nomura, N.Magome, Y.Mori, K.Yoshikkawa
    • Journal Title

      Physical Review E 72

      Pages: 41603-41603

    • NAID

      120000809101

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Metastable and unstable structures in microphase separated diblock copolymers.2005

    • Author(s)
      K.Yamada, M.Nonomura, A.Saeki, T.Ohta
    • Journal Title

      J. Phys. : Condens. Matter 17

      Pages: 4877-4887

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Micro-phase separation in rod-coil copolymers2005

    • Author(s)
      T.Ohta, N.Yamazaki, M.Motoyama, K.Yamada, M.Nonomura
    • Journal Title

      J. Phys. : Condens. Matter 17

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chemotaxis and growth system with singular sensitivity function2005

    • Author(s)
      M.Aida, K.Osaki, T.Tsujikawa, A.Yagi, M.Mimura
    • Journal Title

      Nonlinear Anal. 6

      Pages: 323-336

    • NAID

      120005285846

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Chaotic Pulses for Discrete Reaction Diffusion Systems2005

    • Author(s)
      Y.Nishiura, D.Ueyama, T.Yanagita
    • Journal Title

      SIADS 4(3)

      Pages: 733-754

    • NAID

      120000882186

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Adaptive mesh finite element method for pattern dynamics in reaction-diffusion systems2005

    • Author(s)
      M.Kimura, H.Komura, M.Mimura, H.Miyoshi, T.Takaishi, D.Ueyama
    • Journal Title

      Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005

      Pages: 56-68

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations2005

    • Author(s)
      Y.Giga
    • Journal Title

      nt.J.Pure Appl.Math. 22

      Pages: 165-184

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stability of facets of self-similar motion of a crystal2005

    • Author(s)
      Y.Giga
    • Journal Title

      Adv.Differential Equations 10

      Pages: 601-634

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Metastable and unstable structures in microphase separated diblock copolymers2005

    • Author(s)
      T.Ohta
    • Journal Title

      J.Phys. : Condens.Matter 17

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Signal ion propagation failure in one-dimensional FitzHugh-Nagumo equation2005

    • Author(s)
      T.Yanagita
    • Journal Title

      Phys.Rev.E 71

      Pages: 36226-36226

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Obtainning multiple separate food sources : Behavioural intelligence in the Physarum plasmodium2004

    • Author(s)
      T.Nakagaki
    • Journal Title

      Proc. R. Soc. Lond. B 271

      Pages: 2305-2310

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A PDE approach for motion of phase boundaries by a singular interfacical energy.2004

    • Author(s)
      M.-H.Giga, Y.Giga
    • Journal Title

      Advanced Studies in Pure Mathematics 39

      Pages: 213-232

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Blow up rate for semilinear heat equations with subcritical nonlinearity2004

    • Author(s)
      Y.Giga, S.Matsui, T.Sasayama
    • Journal Title

      Indiana Univ. Math. J. 53

      Pages: 483-514

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence of self-similar evolution of crystals grown from super, saturated vapor2004

    • Author(s)
      Y.Giga, P.Rybka
    • Journal Title

      Interfaces and Free Boundaries 6

      Pages: 405-421

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Local solvability of a constrained gradient system of total variation2004

    • Author(s)
      Y.Giga, Y.Kashima, N.Yamazaki
    • Journal Title

      Abstract and Applied Analysis 8

      Pages: 651-682

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On breakdown of solutions of a constrained gradient system of total variation2004

    • Author(s)
      Y.Giga, H.Kuroda
    • Journal Title

      Boletim da Sociedade Paranaense de Matematica 22

      Pages: 9-24

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Singular diffusivity-facets, shocks and more2004

    • Author(s)
      Y.Giga
    • Journal Title

      ICIAM 2003, Applied-Mathematics Entering the 21st Century, SIAM

      Pages: 121-134

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Kinetics of morphological transitions in microphase-separated diblock copolymers2004

    • Author(s)
      K.Yamada
    • Journal Title

      Macromolecules 37

      Pages: 5762-5777

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 高分子共重合体のメソフェイズ間転移のキネティクス2004

    • Author(s)
      太田 隆夫
    • Journal Title

      機能材料 24

      Pages: 43-47

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 高分子メソフェイズの転移キネティクス2004

    • Author(s)
      野々村 真規子
    • Journal Title

      高分子 53

      Pages: 267-269

    • NAID

      10012706467

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions.2004

    • Author(s)
      E.C.M.Crooks
    • Journal Title

      Nonlinear Analysis, Series A 14

      Pages: 645-665

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Pattern Formation in Consumer-Finite Resource Reaction-Diffusion Systems2004

    • Author(s)
      M.Mimura
    • Journal Title

      Publ. RIMS, Kyoto Univ 40

      Pages: 413-1431

    • NAID

      110001052100

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On some classes of linearizable reaction-convection-diffusion equations2004

    • Author(s)
      M.Rodrigo
    • Journal Title

      Analysis and Applications 110

      Pages: 1-8

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Obtaining multiple separate food sources : Behavioural intelligence in the Physarum plasmodium2004

    • Author(s)
      T.Nakagaki, R.Kobayashi, T.Ueda, Y.Nishiura
    • Journal Title

      Proc. R. Soc. Lond. B 271

      Pages: 2305-2310

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A PDE approach for motion of phase boundaries by a singular interfacial energy2004

    • Author(s)
      M.-H.Giga, Y.Giga
    • Journal Title

      Advanced Studies in Pure Mathematics 39

      Pages: 213-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Blow up rate for semilinear heat equations with subcritical nonlinearity2004

    • Author(s)
      Y.Giga, S.Matsui, S.Sasayama
    • Journal Title

      Indiana Univ. Math. J. 53

      Pages: 483-514

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence of self-similar evolution of crystals grown from super saturated vapor2004

    • Author(s)
      Y.Giga, P.Rybka
    • Journal Title

      Interfaces and Free Boundaries 6

      Pages: 405-421

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On breakdown of solutions of a constrained gradient system of total variation2004

    • Author(s)
      Y.Giga, H.Kuroda
    • Journal Title

      Boletim da Sociedade Paranaense de Matem'atica 22

      Pages: 9-24

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Singular diffusivity-facets, shocks and more2004

    • Author(s)
      Y Giga
    • Journal Title

      ICIAM 2003, Applied Mathematics Entering the 21st Century, SIAM

      Pages: 121-134

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Kinetics of morphological transitions in microphase-separated diblock copolymers2004

    • Author(s)
      K.Yamada, M.Nonomura, T.Ohta
    • Journal Title

      Macromolecules 37

      Pages: 5762-5777

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions.2004

    • Author(s)
      E.C.M.Crooks, E.N.Dancer, D.Hilhorst, M.Mimura, H.Ninomiya
    • Journal Title

      Nonlinear Analysis, Series A

      Pages: 645-665

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Pattern Formation in Consumer-Finite Resource Reaction-Diffusion Systems2004

    • Author(s)
      M.Mimura
    • Journal Title

      Publ. RIMS, Kyoto Univ. 40

      Pages: 413-1431

    • NAID

      110001052100

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On some classes of linearizable reaction-convection-diffusion equations2004

    • Author(s)
      M.Rodrigo, M.Mimura
    • Journal Title

      Analysis and Applications 110

      Pages: 1-8

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Singular diffusivity-facets, shocks and more2004

    • Author(s)
      Y.Giga
    • Journal Title

      ICIAM 2003, Applied Mathematics Entering the 21st Century(eds.T.Funaki, H.Osada)

      Pages: 121-138

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A theoretical and experimental study on the unidirectional motion of a camphor disk2004

    • Author(s)
      M.Nagayama
    • Journal Title

      Physica D 194

      Pages: 151-165

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Kinetics of morphological transitions in microphase-separated diblock copolymers2004

    • Author(s)
      K.Yamada
    • Journal Title

      Macromolecules (Article) 37

      Pages: 5762-5777

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A PDE approach for motion of Phase boundaries by a singular interfacical energy2004

    • Author(s)
      M.-H.Giga
    • Journal Title

      Stochastic Analysis on Large Scale Interacting Systems, Advanced Studies in Pure Mathematics 39

      Pages: 213-232

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Interacting spots in reaction diffusion systems

    • Author(s)
      S-I.Ei, M.Mimura, M.Nagayama
    • Journal Title

      Discrete and Continuous Dynamical Systems 14(1)

      Pages: 31-62

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Mathematical model of the evolution of polycrystalline structures-Manifold-valued equation with singular diffusivity

    • Author(s)
      R.Kobayashi
    • Journal Title

      RIMS Lecture Notes To appear

    • Related Report
      2004 Annual Research Report
  • [Book] Birkhauser, Basel-Boston-Berlin2006

    • Author(s)
      Y.Giga
    • Total Pages
      273
    • Publisher
      Surface Evolution Equations - a level set approach
    • Related Report
      2006 Annual Research Report
  • [Book] パターン形成とダイナミクス2005

    • Author(s)
      三村 昌泰
    • Total Pages
      149
    • Publisher
      東大出版会
    • Related Report
      2005 Annual Research Report

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

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