| 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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| 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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