1999 Fiscal Year Final Research Report Summary
Nonlinear partial differential equations and infinite dimensional dynamical systems
| Project/Area Number |
09440045
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
JEMBO Shuichi Hokkaido Univ. Grad. School of Science, Prof., 大学院・理学研究科, 教授 (80201565)
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| 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)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Ginzburg-Landau equation / Dynamical systems / Reaction-diffusion equation / Surface evolution equation / Crystalline growth / Fokker-Planck equation / System wave equation |
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| 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.
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