1999 Fiscal Year Final Research Report Summary
Study of singularities arising in nonlinear partial differential differential equations and asymptotic methods
| Project/Area Number |
09304019
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tokyo |
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Principal Investigator |
MATANO Hiroshi School of Mathematical Sciences University of Tokyo, Graduate Professor, 大学院・数理科学研究科, 教授 (40126165)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Masahiro ditto, Associate Professor, 大学院・数理科学研究科, 助教授 (50182647)
YANAGIDA Eiji ditto, Associate Professor, 大学院・数理科学研究科, 助教授 (80174548)
FUNAKI Tadahisa ditto, Professor, 大学院・数理科学研究科, 教授 (60112174)
TANIGUCHI Masaharu Faculty of Science, Tokyo Institute of Technology, Lecturer, 大学院・情報理工学研究科, 講師 (30260623)
MIMURA Masayasu Graduate School of Science Hiroshima University, Professor, 大学院・理学研究科, 教授 (50068128)
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| Project Period (FY) |
1997 – 1999
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| Keywords | nonlinear partial differential equations / qualitative theory / diffusion equations / infinite dimensional dynamical systems / parabolic equations / attractor |
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| Research Abstract |
(1) Dynamics of blow-up solutions Some blow-up solutions of a nonlinear heat equation can be continued beyond the blow-up time in a certain weak sense. Matano studied the dynamics of such solutions from the point of view of dynamical systems.
(2) Motion of interfaces with random deviation In a class of diffusion equations involving a small parameter, say ε, solutions develop sharp transition layers, or interfaces, as ε→0. Funaki considered the case where the equation involves a random deviation term.
(3) Estimate of blow-up time in a nonlinear heat equation Yanagida sutdied blow-up phenomena in a nonlinear heat equation and extended the classical results of Fujita and others.
(4) Motion of interface in competition systems Mimura studied the behavior of interfaces that arise in the singular limit of a three-species competition-diffusion system.
(5) Order-preserving systems in the presence of symmetry Matano extended the existing theory on order-preserving dynamical systems in the presence of symmetry. He then applied the general theory to the stability analysis of traveling waves and other problems.
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