Diffusion phenomenon and Wave phenomenon of solutions to the damped wave equation
| Project/Area Number |
25400184
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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 | Waseda University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 消散型波動方程式 / 拡散現象 / 波動現象 / 臨界指数 / 時間大域解 / 解の爆発 / コーシー問題 / 解の大域存在 |
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| Outline of Final Research Achievements |
The solution to the Cauchy problem for the linear wave equation with damping term having constant coefficient is decomposed to the wave part decaying rapidly and the diffusion part. Hence it approaches to the diffusion part as time tends to infinity, which is called the diffusion phenomenon. In the case that the coefficient of damping depends on time or space variables, the damping becomes effective or non-effective by the decaying order in time or space of the coefficient, and the solution to the Cauchy problem still has diffusion phenomenon or it shows wave phenomenon, respectively. The research of diffusion effect has developed. In particular, the critical exponents were obtained for the semilinear damped wave system in a series of joint works with Dr. Yuta Wakasugi. Also, the plenary lecture on these theories was given in the conference WinC 2016 in Sri Lanka.
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Report
(5 results)
Research Products
(15 results)
