2014 Fiscal Year Final Research Report
Relationship between the gloval solvability and a non-lineaer action for a nonlinear damped wave equation
| Project/Area Number |
23740116
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Fukuoka Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 非線形消散型波動方程式 / 非線形消散型梁方程式 / 高次漸近展開 / 時間減衰評価 |
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| Outline of Final Research Achievements |
We studied the relationship between the global solvability and the effect of the nonlinear term for nonlinear partial differential equations with weak damping as represented by a nonlinear damped wave equation. More precisely, we obtained the sufficient condition for the approximation of the solution for a system of nonlinear damped wave equation by the heat kernel. We also considered the large time behavior of the global solutions for nonlinear dispersive equations with the weak damping and the forth order diffusion (nonlinear damped beam equations, the Cahn-Hilliard equation with inertial term, the Falk-Konopka system of shape memory alloys with weak damping).
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| Free Research Field |
偏微分方程式論
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