2005 Fiscal Year Final Research Report Summary
Mathematical analysis for nonlinear partial differential equations with singular solutions
| Project/Area Number |
15340041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 univ., Dept. of Natural Sciences, Prof., 自然科学研究科, 教授 (20214223)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAKAWA Tetsuro Kanazawa univ. Dept. of Natural Sciences, Prof., 自然科学研究科, 教授 (10033929)
JIMBO Shuichi Hokkaido Univ. Dept. of Mathematics, Prof., 大学院・理学研究科, 教授 (80201565)
WEISS Georg The Univ. of Tokyo. Dept. of Mathematical Science, Associate Prof., 大学院・数理科学研究科, 助教授 (30282817)
KIMURA Masato Kyushu Univ. Dept. of Mathematics, Associate Prof., 大学院・数理学研究院, 助教授 (70263358)
KIKUCHI Koji Shizuoka Univ. Dept. of Engneering, Professor, 工学部, 教授 (50195202)
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| Project Period (FY) |
2003 – 2005
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| Keywords | variational problem / nonlinear PDEs / singularity / numerical analysis / minimizing method / free boundary problem |
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| Research Abstract |
The aim of this research was to solve nonlinear Partial Differential Equations whose solution is expected to have singularities depending on time. The candidates of singularities are defects in harmonic mapping, vortex in Ginzburg-Landau problem and free boundaries.
We have solved the following problems;
(1)On a Soap film vibration with free boundary, we have established the method to treat wave type free boundary problems
(2)We developed a numerical method via the discrete Mores flow for volume constraint conditions
(3)We constructed a weak solution to a hyperbolic equation with volume constraint
(4)We constructed a weak solution to a parabolic equation with volume constraint and showing Hoelder continuity of the
solution
Moreover we have developed solvers for parallel machine with minimizing algorithm via the discrete Morese flows. This works very well especially for volume constraint problems. This is also very nice for a weak connected parallel machines, because it uses direct method of variational principle.
Finally, we would like to express pur special thanks to all participants of this project.
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