1998 Fiscal Year Final Research Report Summary
Study of Harmonic Analysis, Solutions to Variational Problems and Partial Differential Equa
| Project/Area Number |
09640208
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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 |
解析学
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| Research Institution | TOKYO METROPOLITAN UNIVERSITY |
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Principal Investigator |
KURATA Kazuhiro Tokyo Metropolitan Unviersity, Assistant Professor, 理学研究科, 助教授 (10186489)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Kazunaga Waseda University, Assistant Professor, 理工学部, 助教授 (20188288)
JIMBO Shuichi Hokkaido Universirty, Professor, 理学研究科, 教授 (80201565)
MURATA Minoru Tokyo Institute of Technology, Professor, 理工学研究科, 教授 (50087079)
SAKAI Makoto Tokyo Metropolitan Unviersity, Professor, 理学研究科, 教授 (70016129)
MOCHIZUKI Kiyoshi Tokyo Metropolitan Unviersity, Professor, 理学研究科, 教授 (80026773)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Super conductivity / Ginzburg-Landau equation / Sem-classical limit / Schrodinger operator / spectrum / elliptic equation / variational problem / singular perturbation problem |
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| Research Abstract |
1. Kurata studied the following :
(1) unique continuation theorem and an estimate of zero set of solutions to Schrodinger operators with singular magnetic fields.
(2) finiteness of the lower spectrum of uniformly elliptic operators singular potentials.
(3) Liouville type theorem for Ginzburg-Landau equation and existence and its profile of the least energy solution to nonlinear Schrodinger equation with magnetic effect.
(4) existence of non-topological solution to a nonlinear elliptic equation arising from Chern-Simons-Higgs theory
2. Jimbo studied existence and zero set of stable non-constant solution to Ginzburg-Landau equation.
3. Tanaka studied Hamilton system, uniquness and non-degeneracy of positive solution to a nonlinea elliptic equation, and the construction of multi-bump solutions.
4. Murata studied uniqueness of non-negative solution to parabolic equation.
5. Mochizuki studied global existence and blow-up of solutions to reaction-diffusion systems.
6. Ishii studied dynamics of hypersurfaces and homogenization of Hamilton-Jacobi equation.
7. Sakai studied Hale-Shaw flow in the case that initial domain has a corner.
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