2001 Fiscal Year Final Research Report Summary
Research of Quasilinear Elliptic and Parabolic Differential Equations
| Project/Area Number |
12640163
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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 | Fukui University of Technology (2001)
Kanazawa University (2000) |
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Principal Investigator |
HAYASIDA Kazuya Fukui Univ. Tech., Prof., 工学部, 教授 (70023588)
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| Co-Investigator(Kenkyū-buntansha) |
ICHINOSE Takashi Kanazawa Univ., Math., Prof., 理学部, 教授 (20024044)
GOTO Shun-ichi Kanazawa Univ., Compt., Assoc. Prof., 理学部, 助教授 (30225651)
OMATA Seiro Kanazawa Univ., Compt., Assoc. Prof., 理学部, 助教授 (20214223)
ISHII Nobuhiko Fukui Univ. Tech., Prof., 工学部, 教授 (20202939)
OGURISU Osamu Kanazawa Univ., Compt., Assoc. Prof., 理学部, 助教授 (80301191)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Cauchy problem / parabolic equation / Dirichlet problem / mean curvature / fast diffusion / H-convexity |
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| Research Abstract |
In this research project we have set up two subjects. The first subject is to research the non-characteristic Cauchy problem for quasilinear parabolic equations. And the second subject is to research the Dirichlet problem of prescribed mean curvature equation.
About the first subject the problem is not well-posed even for the case of linear parabolic equations. So it is important to show that the uniqueness. For the linear case the main method is to use the pseudo differential operators. But for the non-linear case we can not use such a method. In this research project we have devised another method and we have applied it to prove the uniquness for solutions of the quasilinear degenerat parabolic equation, whose typical model is the fast diffusion.
About the second subject there are many papers treating the existence of solutions upto now. In these the essential condition is imposed on the boundary, that is, H-convexity condition. In this research project we have tried to remove such a condition and we have proved that a portion of the boundary is not necessary to satisfy H-convexity condition under some assumptions on the exterior force. And we have applied this result to the case of annular domains.
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Research Products
(9 results)
