Study on interfacial phenomena in nonlinear partial differential equations
| Project/Area Number |
21740113
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Iwate University (2011)
The University of Tokyo (2009-2010) |
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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) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 関数方程式論 / 偏微分方程式 / 界面現象 / パターン形成 |
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| Research Abstract |
In this study, we analyzed the asymptotic stability of planar waves and the large time behavior of disturbed planar fronts that appear in a reaction diffusion equation with bistable type nonlinearity. We improved some previous results and showed the approximation theorem for the large time behavior of planar fronts based on the mean curvature flow. The motion of hypersurfaces governed by the mean curvature flow was also studied, and some sufficient conditions for the asymptotic stability of hyperplanes as traveling wave solutions were shown.
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Report
(4 results)
Research Products
(11 results)
