2002 Fiscal Year Final Research Report Summary
Study of Solutions to Partial Differential Equations, Variational Problems and Inverse Problems
| Project/Area Number |
13640183
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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 |
Basic analysis
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| Research Institution | TOKYO METROPOLITAN UNIVERSITY |
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Principal Investigator |
KURATA Kazuhiro Tokyo Metropolitan University Graduate School of Science Professor, 理学研究科, 教授 (10186489)
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| Co-Investigator(Kenkyū-buntansha) |
MURATA Minoru Tokyo Institute of Technology Graduate School of Science Professor, 大学院・理工学研究科, 教授 (50087079)
SAKAI Makoto Tokyo Metropolitan University Graduate School of Science Professor, 理学研究科, 教授 (70016129)
MOCHIZUKI Kiyoshi Chuo University Faculty of Science Professor, 理工学部, 教授 (80026773)
TANAKA Kazunaga Waseda University Faculty of Science Professor, 理工学部, 教授 (20188288)
JIMBO Shuichi Hokkaido University Graduate School of Science Professor, 大学院・理学研究科, 教授 (80201565)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Cahn-Hilliard energy / Chern-Simons-Higgs theory / optimization problem / first Dirichlet eigenvalue / Ginzburg-Landau equation / Martin boundary / inverse spectrum problem / Hale-Shaw flow |
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| Research Abstract |
1. Kurata studied the following:
(1) breakdown of the monotonicity of the minimizer to a one-dimensional Cahn-Hilliard energy with inhomogeneous weight and the existence of non-topological solution to a nonlinear elliptic equation arising from Chern-Simons-Higgs theory.
(2) optimal location of a obstacle in an optimization problem for the first Dirichlet eigenvalue to Schrodinger operator.
2. Jimbo studied the existence of stable vortex solutions and the non-existence of permanent current in a convex domain to Ginzburg-Landau equation with magnetic effect. Tanaka constructed solutions with complex patterns to inhomogeneous Allen-Cahn equation and nonlinear Schrodinger equation. Murata studied the structure of positive solutions to elliptic equation of skew-product type and classifies the Martin boundary and Martin kernel completely.
3. Mochizuki studied the inverse spectrum problem for Dirac operator and Sturm-Liouville operator by interior datas. Sakai studied the asymptotic behavior of the moving boundary for Hale-Shaw flow when the initial region has an angle in details.
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