2004 Fiscal Year Final Research Report Summary
A study on asymptotic behavior of solutions for evolution equations
| Project/Area Number |
14540208
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
IKEHATA Ryo Hiroshima University, Graduate School of Education, Associate Professor, 大学院・教育学研究科, 助教授 (10249758)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHITA Mishio Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80214633)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Wave equation / exterior domain / Energy / decay / asymptotics of solutions |
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| Research Abstract |
We first discussed the possibility of applications of the device due to Ikehata-Matsuyama (which was newly developed in 1999) to some evolution equations in unbounded domains. For this we have obtained several results concerning the global well-posedness result of damped wave equations with the Fujita type power nonlinearity. And also by the device we have obtained the new result concerning the diffusion phenomenon of abstract second-order evolution equations.
Second we have found the new decay estimates of (semilinear) damped wave equations, which are dealt with in the N-dimensional half space.
Third, by the two methods due to Ikehata-Matsuyama above and Todorova-Yordanov we have succeeded in removing the compactness of the support on the initial data in order to obtain local energy decay estimates of the wave equation in an exterior domain with a star-shaped complement. This result completely generalizes that obtained by Morawetz in 1961. It should be pointed out that the method used to derive local enegy decay results has many wide applications to hyperbolic equations in exterior domains.
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