1998 Fiscal Year Final Research Report Summary
Mathematical Analysis of free boundary problems related to a variational problem
| Project/Area Number |
09640170
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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 | Kanazawa University |
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Principal Investigator |
OMATA Seiro Kanazawa University, Departmnet of Science, Associate Professor, 理学部, 助教授 (20214223)
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| Co-Investigator(Kenkyū-buntansha) |
GOTO Shunichi Kanazawa University, Department of Science, Associate Professor, 理学部, 助教授 (30225651)
TAMURA Hiroshi Kanazawa University, Department of Science, Associate Professor, 理学部, 助教授 (80188440)
FUJIMOTO Hirotaka Kanazawa University, Department of Science, Professor, 理学部, 教授 (60023595)
ICHINOSE Takashi Kanazawa University, Graduate School of Natural Science, Professor, 自然科学研究科, 教授 (20024044)
HAYASIDA Kazuya Kanazawa University, Graduate School of Natural Science, Professor, 自然科学研究科, 教授 (70023588)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Free boundary problem / Variational problem / Nonlinear partial differential equations / Numerical Analysis / Minimizing methods / Superconductivity / Liquid crystals |
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| Research Abstract |
We mainly investigated a free boundary problem related to a variational problem. Since our problem has a feature (hat the free boundary is a set of singular points of a minimizer and the energy concentrate on it. So, we can cosider that our purpose is on treating the energy concentration phenomena on the singularity of solutions. In this stand point of view, we treated the following type of problems :
(1)Develop Regularity theory of elliptic free boundary problem related to minimizing functional with moving boundary,
(2)Develop a Numerical method via a minimization process,
(3)Develop a method related to solve a hyperbolic free boundary problem.
For problem (1), in 2-dimensional case, we successfully showed regularity of free boundary on some nonlinear case. For (2), we treated the Ginzburg-Landau functional which mainly appear in superconducting phenomema. In this, we developed a method due to discrete Morse semiflow for parabolic and hyperbolic problems. For (3), we constucted a strong solutions related to hyperbolic free boundary problems under some compatibility conditions. Moreover we developed a software to solve this with good accuracy. We summed up these results into 7 papers (appeared or in press) and I preprint (submitted).
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