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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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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 / 時間大域可解性 / 解の漸近挙動 / 高次漸近解析 |
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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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Report
(5 results)
Research Products
(24 results)
