2013 Fiscal Year Final Research Report
Local smoothing estimates and applications to nonlinear hyperbolic equations
Project/Area Number |
23540198
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Mie University |
Principal Investigator |
HIDANO Kunio 三重大学, 教育学部, 准教授 (00285090)
|
Project Period (FY) |
2011 – 2013
|
Keywords | 非線形波動方程式 / 準線形波動方程式 / 半線形波動方程式 / 初期値問題 / 解の初期値への連続依存性 / 解の最大存在時間 / 時間大域解の存在 |
Research Abstract |
The problem of local well-posedness was studied for quasi-linear wave equations with low-regularity radially symmetric data. Emphasis was on the investigation of continuous dependence of solutions on initial data. Combined effects of some two nonlinear terms in the lifespan of small solutions to semilinear wave equations were also studied. Further, the Cauchy problem was studied for systems of quasi-linear wave equations with multiple speeds in two space dimensions. The localized energy estimate for constant-coefficient linear wave equations played a key role in giving an alternative proof of global existence of small solutions.
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