2010 Fiscal Year Final Research Report
Classification of nonlinearities of reaction-diffusion systems from a dynamical viewpoint
| Project/Area Number |
20540144
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ryukoku University |
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Principal Investigator |
NINOMIYA Hirokazu Ryukoku University, 理工学部, 准教授 (90251610)
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| Co-Investigator(Renkei-kenkyūsha) |
IIDA Masato 宮崎大学, 工学部, 教授 (00242264)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 反応拡散系 / 爆発問題 / 解の大域的存在 / 急速反応極限 / 進行波解 / 全域解 |
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| Research Abstract |
To classify the nonlinearities of reaction-diffusion systems, we studied the following researches. We derive the limit problem from some reaction-diffusion systems by using the fast reaction limit and discuss the relationship between the degeneracy of nonlinearity and the limit problem. We also constructed non-planar traveling waves of Allen-Cahn equations or the free boundary value problem which comes from some reaction-diffusion system, which are of finger type and of spot type. We also studied the imperfect bifurcation of some elliptic problem under the perturbation of the domain.
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