2017 Fiscal Year Final Research Report
Global existence and the asymptotic behavior for partial diffierential equations concerning nonlinear waves
| Project/Area Number |
26400168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Osaka University (2016-2017)
Wakayama University (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 非線形波動方程式 / 大域解 / 零条件 / 弱零条件 / 漸近挙動 |
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| Outline of Final Research Achievements |
We studied sufficient conditions for the existence of global solutions (solutions up to the arbitrary time) to the Cauchy problem for systems of nonlinear wave equations, or for some related systems, with small initial data. Concerning sufficient conditions weaker than the well-known null condition (such weaker conditions are called the "weak" null conditions), we unified the two known "weak" null conditions, and proved the global existence under this unified condition. Some formula to give the asymptotic behavior for global solutiuons was obtained. We also improved the global existence theorem by Alinhac for wave equations in two space dimensions. Concerning the systems of nolinear wave and Klein-Gordon equations, we proved the global existence of solutions under a weaker condition than before, in the case that initial data vanish outside a bounded region.
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| Free Research Field |
非線形偏微分方程式
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