2001 Fiscal Year Final Research Report Summary
Study of asymptotic behavior of solutions of differential equations
| Project/Area Number |
12640215
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
TAKAKUWA Shoichiro Tokyo Metropolitan University, Graduate School of Science, Assosiate Professor, 大学院・理学(系)研究科(研究院), 助教授 (10183435)
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| Co-Investigator(Kenkyū-buntansha) |
SUMI Naoya Graduate School of Science, Assistant Professor, 大学院・理学(系)研究科(研究院), 助手 (50301411)
HIDANO Kunio Graduate School of Science, Assistant Professor, 大学院・理学(系)研究科(研究院), 助手 (00285090)
KURATA Kazuhiro Graduate School of Science, Assosiate Professor, 大学院・理学(系)研究科(研究院), 助教授 (10186489)
NAKAUCHI Nobumitsu Yamaguchi University, Department of Mathematical Sciences,Associate Professor, 理学部, 助教授 (50180237)
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| Project Period (FY) |
2000 – 2001
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| Keywords | differntial equation / asymptotic behavior / variational problem / scattering theory / dynamical system / harmonic map / Cauchy problem / fundamental solution |
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| Research Abstract |
Our results of this reserch project are the following.
1 We study harmonic maps between two Riemannin manifolds.
(1) We prove the Liouville type theorem for harmonic maps. By applying Liouville type theorem As an application of this theorem, we obtain the estimate of the gradients of singular harmonic maps using the distance from the set of singular points.
(2) We prove the uniqueness theorem of the Dirichlet boundary value problem for harmonic maps defined on bounded domain in Euclidean space. And we have a similar result to more general nonlinear elliptic systems.
2 We show the existence of the non-topological solution of the nonlinear elliptic equation appearing the Chern-Simons-Higgs theory.
3 We investigate the asymptotic behavior of the semi-linear wave equation as time goes to infinity. We obtain the results related to the scattering and the self-similarity of the solution.
4 We obtain the lower bound of the first eigenvalue of the p-Laplace operator on Riemannian manifolds.
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