Studies on the sufficient conditions for the global existence of solutions to the exterior problems for nonlinear hyperbolic equations
| Project/Area Number |
20540211
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Wakayama University |
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Principal Investigator |
KATAYAMA Soichiro Wakayama University, 教育学部, 教授 (70283942)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 非線形波動方程式 / 零条件 / 大域解 / 外部問題 / クラインーゴルドン方程式 / 双曲型方程式 / 波動方程式 / 非線形 / クライン-ゴルドン方程式 / null条件 / 漸近挙動 / 初期値境界値問題 |
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| Research Abstract |
We consider the exterior problem for the linear wave equations, and obtained the convergence rate of the solution to its asymptoics. As an application, we also obtained the precise lower bound estimate of the lifespan of the solutions to the exterior problem for semilinear wave equations. We investigated the asymptotic behavior of global solutions to the systems of nonlinear wave equations with multiple propagation speeds. In connection to the exterior problem, we also study the Cauchy problem in the whole space for various kinds of nonlinear systems, such as systems of wave or Klein-Gordon equations and coupled systems of these equations, and investigated the condition for the global existence of solutions and their asymptotic behavior.
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Report
(4 results)
Research Products
(15 results)
