2000 Fiscal Year Final Research Report Summary
Mathematical Analysis of partial differential equations related to a variational problem via the discrete Morse Semiflows
| Project/Area Number |
11640159
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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 | Kanazawa University |
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Principal Investigator |
OMATA Seiro Kanazawa University, Department of Science, Associate Professor, 理学部, 助教授 (20214223)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIMOTO Hirotaka Kanazawa University, Department of Science, Professor, 理学部, 教授 (60023595)
ICHINOSE Takashi Kanazawa University, Department of Science, Professor, 理学部, 教授 (20024044)
HAYASIDA Kazuya Kanazawa University, Department of Science, Professor, 理学部, 教授 (70023588)
GOTO Shun'ichi 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)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Variational problem / Nonlinear partial differential equations / Numerical Analysis / Minimizing methods / Free boundary problem |
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| Research Abstract |
We mainly investigated partial differential equations related to a variational problem via the discrete Morse semiflows. Our main interest is on sets of singular points of a solutions. Such sets has sometimes big 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 a prallel machine for solving mininizing problems,
(2) Develop a Numerical method via a minimization process,
(3) Develop a method to solve both parabolic and hyperbolic equations via minimizing.
For these problems, we have developped a 8-CPU parallel computer for solving minimizing problems. By use of this, we did a numerical copmutations to catch the structure of singularities for eikonal equation, Ginzburg-Landau system, and smestics liquid crystal problems. Basic method due to discrete Morse semiflow for parabolic and hyperbolic problems.
We also solved the asymptotic behavior of solitary wave solutions for BBM-Burgers equations.
Moreover we developped a software to solve hyperbolic free boundary problems. This is based on the smoothing method of a equation and we can get good results even when the free boundary changes its topology.
We summed up these results into 8 papers (appeared or in press) and 2 preprint (submitted).
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Research Products
(16 results)
