2011 Fiscal Year Final Research Report
Structure of solution spaces for singular partial differential equations.
| Project/Area Number |
20540197
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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 | Saga University |
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Principal Investigator |
KAJIKIYA Ryuji 佐賀大学, 工学系・研究科, 教授 (10183261)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 関数方程式 / 非線形偏微分方程式 |
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| Research Abstract |
(1) We prove the existence of solutions for semilinear elliptic equations with the singular weight on the boundary. We prove the existence of a smooth positive solution and infinitely many sign-changing solutions.(2) We prove that the bifurcation occurs for one-dimensional p-Laplace equations with singular weights on the boundary.
(3) For degenerate parabolic equations with the infinity Laplacian, we prove that solutions decay as time tends to infinity and investigate the decay order in detail.
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