2013 Fiscal Year Final Research Report
Research for Critical Asymptotic Structure of Nonlinear Evolution Equations
| Project/Area Number |
20244009
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
OGAWA Takayoshi 東北大学, 理学(系)研究科(研究院), 教授 (20224107)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHIMA Shuichi 九州大学, 数理学研究院, 教授 (70144631)
MISAWA Masashi 熊本大学, 自然科学研究科, 教授 (40242672)
TAKAGI Izumi 東北大学, 理学研究科, 教授 (40154744)
ISHIGE Kazuhiro 東北大学, 理学研究科, 教授 (90272020)
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| Project Period (FY) |
2008-04-08 – 2013-03-31
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| Keywords | 非線形ｼｭﾚﾃﾞｨﾝｶﾞｰ方程式 / 時間局所適切性 / 斉次Besov空間 / モデュレーション空間 / 退化移流拡散方程式 / ソボレフ臨界指数 / 質量臨界 / 有限時刻爆発 |
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| Research Abstract |
The main reseacher T. Ogawa researched several nonlinear partial differential equations with critical structure and find various criticality in each problems. He studied the following topics with colabolators. Two dimensional drift-diffusion system in the critical Besov spaces and established maximal regularity for the heat equation in non-reflexivie Banach spaces. Higher order expansion of the solution for the drift-diffusion system in higher space dimensions, the global existence for the nonlinear damped wave system, the critical Sobolev inequality with logarithmic type and generalization to abstract Besov spaces, WKB approximation for nonlinear Schrodinger equations with Poisson equations, the scaling critical solvabilityfor quadratic nonlinear Schrodinger equation and critical well-posedeness in lower space dimensions.
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