2010 Fiscal Year Final Research Report
Analysis of interface motion and blow-up phenomena in nonlinear partial differential equations
| Project/Area Number |
20340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | The University of Tokyo |
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Principal Investigator |
MATANO Hiroshi The University of Tokyo, 大学院・数理科学研究科, 教授 (40126165)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Kenーichi 電気通信大学, 電気通信学部, 助教 (40293120)
WEISS Georg S. 東京大学, 大学院・数理科学研究科, 准教授 (30282817)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 非線形問題 / 非線形偏微分方程式 / 進行波 / 特異性 / 界面運動 / 解の爆発 / 電気生理学 |
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| Research Abstract |
This research project deals with such themes as (1) traveling waves in nonlinear diffusion equations, (2) singular limit of nonlinear diffusion equations and interface motion, (3) blow-up in nonlinear heat equations, (4) mathematical analysis of 3D cellular electrophysiological model. The theme (4) was added after the program began. In theme (1), we studied, among other things, traveling waves colliding with obstacles, the stability of planar waves, and the problem of maximizing traveling wave speeds. In theme (3) we studied, among other things, classification of blow-up in Sobolev superlinear heat equations, and an application the theory of braid groups to the dead-core problem.
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