2005 Fiscal Year Final Research Report Summary
Study of the structure of solutions to Variational Problems, Inverse Problems and Partial Differential Equations
| Project/Area Number |
15540177
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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, Faculty of Urban Liberal Arts, Professor, 都市教養学部理工学系, 教授 (10186489)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAI Makoto Tokyo Metropolitan University, Faculty of Urban Liberal Arts, Professor, 都市教養学部理工学系, 教授 (70016129)
OKADA Masami Tokyo Metropolitan University, Faculty of Urban Liberal Arts, Professor, 都市教養学部理工学系, 教授 (00152314)
ISOZAKI Hiroshi Tsukuba University, Graduate School of Science, Professor, 数理物質科学研究科, 教授 (90111913)
TANAKA Kazunaga Waseda University, Graduate School of Scieace, Professor, 理工学術院, 教授 (20188288)
JIMBO Shuichi Hokkaido University, Graduate School of Science, Professor, 理学研究科, 教授 (80201565)
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| Project Period (FY) |
2003 – 2005
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| Keywords | optimization problem / variational problem / singular perturbation problem / nonlinear Schroedinger equation / numerical simulation / inverse conductivity problem / free boundary problem / spectrum |
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| Research Abstract |
1. Kurata studied the existence and qualitative properties of optimal solutions to several optimization problems for nonlinear elliptic boundary value problems arising in mathematical biology and nonlinear heat conduction phenomena. Kurata also proved the existence of multiple stable patterns in population growth model with Allee effect, symmetry breaking phenomena of the least energuy solution to nonlinear Schroedindger equation and asymptotic profile of radial solution with vortex to 2-dimensional nonlinear Schroedinger equation.
2. Okada studied numerial simulation and numerical analysis of nonlinear paratial differential equations. Especially, he constructed boundary spline function by using Newton extrapolation polynomials.
3. Sakai studied Hele-Shaw free boundary problem in the case that initial data has a cusp and found sufficient conditions to specify the typical pheneomena.
4. Isozaki discovered the relationship between the hyperbolic geometry and inverse problem. He also studied the inverse conductivity problem with discontinuous inclusions and found a numerical algorithm to detect discontinuities.
5. Jimbo continued his research on the study of solution structure of the Ginzburg-Landau equation arising in superconductivity under heterogeneous environments. He also studied the spectrum of elliptic operator associated with the Maxwell equation and proved characterization of eigenvalues and proved a perturbation formula by using weak forms.
6. Tanaka studied concentration phenomena of solutions and clustered solutions for nonlinear elliptic singular perturbation problems. Especially, he constructed high frequency solution to nonlinear Schroedinger equations and multi-clustered high energy
Solutions to a phase transition prolem.
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Research Products
(95 results)
