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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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 関数方程式 / 非線形偏微分方程式 / 劣線形楕円型偏微分方程式 / p-ラプラシアン / 解の分岐 / 特異楕円形偏微分方程式 / 正値解 / 解の正則性 / 固有値問題 / 優線形楕円型偏微分方程式 / 比較定理 / 無限大ラプラス作用素 / 粘性解 / 薄い領域 / 正値解の一意性 / 解の漸近挙動 / 変数分離解 / 解の減衰 |
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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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Report
(6 results)
Research Products
(76 results)
