2013 Fiscal Year Final Research Report
Energy decay for hyperbolic partial differential equations with variable coefficients and its related topic
| Project/Area Number |
22540193
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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 |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
IKEHATA Ryo 広島大学, 教育学研究科(研究院), 教授 (10249758)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 波動方程式 / 摩擦項 / エネルギー減衰 / マルチプライアー法 / フーリエ変換 / 拡散構造 |
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| Research Abstract |
We discovered the existence of the double structure in the wave equations with da-mping terms decaying critically near infinity from the viewpoint of the energy decay rates. Secondly we
caught the asymptotic profile of solutions to the strongly damped wave equations in the abstract framework. Thirdly, we derived precise decay estimates of solutions to the wave equations with non-local terms, wh-ich interpolates the weak and strong damping. Finally, we constructed a new modified energy method in the
Fourier space, and the method could be well applied to the several concrete models in order to get the (almost) optimal decay estimates of solutions.
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