2009 Fiscal Year Final Research Report
Research on evolution equations involving nonlinear Laplace operators
| Project/Area Number |
19740073
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Shibaura Institute of Technology |
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Principal Investigator |
AKAGI Goro Shibaura Institute of Technology, システム理工学部, 准教授 (40433768)
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| Project Period (FY) |
2007 – 2009
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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 |
Sufficient conditions for the existence of local (in time) solutions of some evolution equations involving p-Laplace operators are obtained. Moreover, the well-posedness of some evolution equation involving the infinity-Laplace operator is proved, and furthermore, the asymptotic behaviors (e.g., decay rates) of solutions are also revealed. Finally, a couple of effective methods are established in order to construct solutions and analyze their large-time behaviors for evolution equations involving nonlinear Laplace operators through this research project.
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