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1999 Fiscal Year Final Research Report Summary

Nonlinear partial differential equations and infinite dimensional dynamical systems

Research Project

Project/Area Number 09440045
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

JEMBO Shuichi  Hokkaido Univ. Grad. School of Science, Prof., 大学院・理学研究科, 教授 (80201565)

Co-Investigator(Kenkyū-buntansha) HAYASHI Mikihiro  Hokkaido Univ. Grad, School of Sci., Prof., 大学院・理学研究科, 教授 (40007828)
NAKAZI Takahiko  Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (30002174)
GIGA Yoshikazu  Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (70144110)
MORITA Yoshihisa  Ryukoku Univ. Faculty of Tech. Sci.. Prof., 理工学部, 教授 (10192783)
MIKAMI Tosio  Hokkaido Univ. Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (70229657)
Project Period (FY) 1997 – 1999
KeywordsGinzburg-Landau equation / Dynamical systems / Reaction-diffusion equation / Surface evolution equation / Crystalline growth / Fokker-Planck equation / System wave equation
Research Abstract

(I) Stable solutions and their domain dependency of the Ginzburg-Landau equation are studied. Solutions with vortices and topologically various kinds of solutions are
(ii) Nonstationary complex Ginzburg-Landau equation and its time periodic solutions are studied. The stability of the solutions and dependence on the domains are investigated. Constructed pattern formation under the non-uniform environment is studied.
(iii) Nonstationary Ginzburg-Landau equation and its dynamical system of singular perturbation problem is studied. Particularly, it is represented as a finite dimensional ODE and its formula is explicitly obtained.
(iv) Homoclinic orbits arising in reaction-diffusion equations are studied. The bifurcation of the dynamical structure is studied.
(v) Dynamical system arising in surface evolution equations such as mean curvature flow, surface diffusion equations are studied. Asymptotic behavior and geometrical property are analyzed.
(vi) Global existence of solutions in wave equation system with component different propagation speeds is studied.
(vii) Fast diffusion equations and their extinction phenomena are studied.
(viii) Random crystalline evolution equation is studied
(ix) The eigenvalue problem of the Laplacian and the semilinear eiliptic equations on a domain with partial degeneration are studied. More general cases of the singular perturbation of domains are dealt with and the results known before are extended.

  • Research Products

    (48 results)

All Other

All Publications (48 results)

  • [Publications] S.JIMBO: "On the existence of nontrivial stable solutions to the Ginzburg-Landau equation"NONLINEAR ANALYSIS. 30. 811-817 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.JIMBO: "Ginzburg-Landau equation with magnetic effect : Non-simply-connected domains"J.Math.Soc.Japan. 50. 663-684 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Y.Chen: "Stabilization of vortices in the Ginzburg-Landau equation with variable diffusion coefficients"SIAM J.Math.Anal. 29. 903-912 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.JIMBO: "Stable vortex solutions to the Ginzburg-Landau equation with a variable diffusion coefficientinadisk"J.Differential Equations. 155. 153-176 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Morita: "Stability of solutions to the Ginzburg-Landau equation with Neumaun condiction"NONLINEAR ANALYSIS. 30. 3939-3946 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Morita: "Stable solutions with zeros to the Ginzburg-Landau equation"Proceedings of the US-Chinese Conference Differential Equations and Application, International Press. 227-232 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Morita: "Homoclinic bifurcations in a diffusively coupled excitable system"Fields Institute Communications. 21. 397-407 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.G.Chen: "On instant extinction for very fast diffusion equations"Discrete and continuous Dynamical Systems. 3. 243-250 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.GIGA: "A level set method for surface evolution equations"Sugaku Expositions. 10. 217-241 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.NAKAZI: "Invarian subspace theorems for subdiagonal algebras"J.Operator Theory. 37. 379-395 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.NAKAZI: "Weighted norm inequalities for some singular integral operators"J.Funct.Anal.. 148. 279-295 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.NAKAZI: "The commutator ideal in Toeplitz algebras for uniform algebras and the analytic structure"Arch.Math.. 69. 221-226 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.NAKAZI: "The spectra of Toeplitz operators with unimodular symbols"Proc.Edinburgh Math.Soc.. 41. 133-139 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.NAKAZI: "Brown-Halmos type theorems of weighted Toeplitz operators"Canad.Math.Bull.. 41. 196-206 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.HAYASHI: "Classification of Riemann surface with a nonconstant meromorphic function bounded at infinity"Izvestiya Natsionalnoi Akademii Nauk Armeneii.Mathematicheska. 32. 37-44 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.HAYASHI: "Point separation of a two-sheeded disc by bounded analytic functions"Hokkaido Math.J.. 76. 109-136 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.HAYASHI: "A uniqueness theorem and the Myrberg type phenomenon"J.d'Analyse Math.. 76. 109-136 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.HAYASHI: "Bounded analytic functions on Riemann surfaces"Aspect of Complex Analysis, Differential Geometry, Mathematical Physics and Application. 45-59 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.MIKAMI: "Weak convergence on the first exit time of randomly perturbed dynamical system with a repulsive equilibrium point"Hokkaido Math.J.. 26. 669-684 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.MIKAMI: "Asymptotic behavior of the first exit time of randomly perturbed dynamical systems with a repulsire equilibrium point"J.Math.Soc.Japan. 50. 95-117 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.MIKAMI: "Equivalent conditions on the central limit theorem for a sequence of probability measures on R."Statist.Prob.Lett.. 37. 237-242 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.HONDA: "Stokes phenomena of holonomic systems"数理研講究録. 1014. 21-31 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.HONDA: "Microfunction Solutions of holonomic systems with irregular singularities"New Trends in Microlocal Analysis. 191-205 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.HONDA: "Microlocal stokes phenomena for holonomic modules"Toward the exact WKB analysis of differential equations, Kyoto Univ.Press. 102-131 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Jimbo: "On the existence of nontrivial stable solutions to the Ginzburg-Landau equation"Nonlinear Anal. TMA. 30. 811-817 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Jimbo: "Ginzburg-Landau equation with magneticeffect : Non-simply-connected domams"J. Math. Soc. Japan. 50. 663-684 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X.Y.Chen: "Stabilization of vortices in the Ginzburg-Landau equation with variable diffusion coefficients"SIAM J. Math. Anal.. 29. 903-912 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Jimbo: "Stable vortex solutions to the Ginzburg-Landau equation with a variable diffusion coefficient in a disk"J. Differential Equation. 155. 153-176 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Morita: "Stability of solutions to the Ginzburg-Landau equation with Neumann condition"Nonlinear Anal TMA. 30. 3939-3946 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Morita: "Stable solutions with zeros to the Ginzburg-Landau Equation under Neumann condition"Proceedings of the US-Chinese Conference, Differential Equations and Applications, Eds. P. W. Bates, S-N. Chow, K. Lu and X. Pan, International Press. 227-232 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Morita: "Homoclinic biforcation in a diffusively coupled excitable system, Conference on Differential Equations with Applications to Biology. Eds., S. Ruan, G. Wolkowicz and J. Wu"Fields Institute Commucations. 21. 397-407 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. G. Chen: "On instant extinction for very fast diffusion Equation"Discrete and continuous Dynamical Systems. 3. 243-250 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Giga: "A level set method for surface evolution equations"Sugaku Expositions. 10. 217-241 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Nakazi: "Invariant subspace theorems for subdiagonal algebras"J. Operator Theory. 37. 379-395 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Nakazi: "Weighted norm inequalities for some singular integral operators"J. Funct. Anal.. 148. 279-395 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Nakazi: "The commutator ideal in Toeplitz algebras for uniform algebras and the analytic structure."Arch. Math.. 69. 221-226 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T, Nakazi: "The spectra of Toeplitz operators with unimodular symbols"Proc. Edinburgh Math. Soc.. 41. 133-139 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Nakazi: "Brown-Halmos type theorems of weighted Toeplitz operator"Canad. Math. Bull.. 41. 196-206 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Hayashi: "Classification of Riemann surfaces with a nonconstant meromorphic function bounded at infinity"Izvestiya Natsionalnoi Akademii Nauk Armenii. Mathematicheska 32, 37-44, 1997 ; J. Contemporary Mathematical Analysis" by Allerton Press, Inc.. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Hayashi: "Point separation of a two-sheeted disc by bounded analytic functions"Hokkaido Math. J.. 76. 109-136 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Hayashi: "A uniqueness theorem and the Myrberg type phenomenon"J. d'Analyse Math. 76. 109-136 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Hayashi: "Boonded Analytic function of Riemann Surfaces, Aspect of complex analysis, differential geometry"Mathematical Physics and Application. 45-59 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Mikami: "Weak convergence on the first exit time of randomly perturbed dynamical systems with a repulsive equilibrium point"Hokkaido Math. J.. 26. 669-684 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Mikami: "Asymptotic behavior of the first exit time of randomly perturbed dynamical systems with a repulsive equilibrium point"J. Math. Soc Japan. 50. 95-117 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Mikami: "Equivalent conditions on the central limit theorem for a sequence of probability measures on R"Statist. Prob. Lett.. 37. 237-242 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Honda: "Stokes phenomena of holonomic systems"SUURIKEN KOKYUROKU. 1014. 21-31 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Honda: "Microfunction Solutions of holonomic systems with irregular singularities"New Trends in Microlocal Analysis. (Springer). 191-205 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Honda: "Microlocal stokes phenomena for holonomic module"Toward the exact WKB analysis of differential equations, Kyoto Univ. Press. 102-131 (1999)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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