| Project/Area Number |
25800071
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Iwate University |
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Principal Investigator |
Nara Mitsunori 岩手大学, 人文社会科学部, 准教授 (90512161)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 偏微分方程式 / 反応拡散方程式 / 界面現象 / 進行波 / 擬微分方程式 / パターン形成 / 偏微分方程式論 |
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| Outline of Final Research Achievements |
This research mainly deals with the following topics; (1) singular limit problem of damped wave equations with bistable-type nonlinearity on the multi-dimensional whole space, where some estimates for generation and motion of interfaces are obtained, (2) stability of one-dimensional traveling wave solutions in the damped wave equations with bistable-type nonlinearity is analyzed, and some sufficient conditions for such the stability is shown, (3) asymptotic behavior of solutions with spreading fronts in the Cauchy problem of anisotropic Allen-Cahn equations is studied, where it is revealed that the notions of Frank diagram and Wulff shape play important roles.
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