1999 Fiscal Year Final Research Report Summary
CHARACTERISTIC BOUNDARY VALUE PROBLEM FOR LINEAR AND NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS
| Project/Area Number |
09440061
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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 |
解析学
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| Research Institution | OSAKA INSTITUTE OF TECHNOLOGY (1999)
Nara Women's University (1997-1998) |
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Principal Investigator |
SHIZUTA Yasushi OSAKA INSTITUTE OF TECHNOLOGY, FACULTY OF INFORMATION SCIENCE, PROFESSOR, 情報科学部, 教授 (90027368)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Mayumi (大野 真弓) HYOGO UNIVERSITY, FACULTY OF ECONOMICS AND INFORMATION SCIENCE, ASSOCIATE PROFESSOR, 経済情報学部, 助教授 (00271479)
TOMOEDA Kenji OSAKA INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (60033916)
KASAHARA Kouji OSAKA INSTITUTE OF TECHNOLOGY, FACULTY OF INFORMATION SCIENCE, PROFESSOR, 情報科学部, 教授 (70026748)
SHINODA Masato NARA WOMEN'S UNIVERSITY, FACULTY OF SCIENCE, ASSISTANT PROFESSOR, 理学部, 講師 (50271044)
YANAGISAWA Taku NARA WOMEN'S UNIVERSITY, FACULTY OF SCIENCE, ASSOCIATE PROFESSOR, 理学部, 助教授 (30192389)
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| Project Period (FY) |
1997 – 1999
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| Keywords | symmetric hyperbolic system / characteristic boundary value problem / regularity theorem for the solution / nonlinear diffusion equation / splitting of the support of solutions |
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| Research Abstract |
(1) We obtained a final form of the regulatory theorem for solutions to the initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Combining the continuation of "local" solution argument with the results which have be established earlier, we reached a new result. We can say now that the linear theory is completed. As for the quasi-linear case, the result of our study is still poor. There are many things to do in studying this problem.
(2) We studied the nonlinear diffusion equation with strong absorption term. We have been mainly interested in the phenomenon, called the splitting of the support of solutions. Mathematically, this can be regarded as a moving boundary problem. We succeeded in constructing a good scheme for the numerical analysis of the equations.
Thus we were able to find a sufficient conclusion under which the splitting of the support of solutions occurs.
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