2009 Fiscal Year Final Research Report
On a study of a solution with a transition layer for a bistable reaction diffusion equation with a heterogeneous environment
| Project/Area Number |
20740098
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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 | Numazu College of Technology |
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Principal Investigator |
MATSUZAWA Hiroshi Numazu College of Technology, 教養科, 講師 (80413780)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 偏微分方程式 / 反応拡散方程式 / 双安定 / 遷移層 / 不変多様体 |
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| Research Abstract |
In this research we study the dynamics of a single transition layer of a solution to a spatially inhomogeneous bistable reaction diffusion equation in one space dimension. The spatial inhomogeneity is given by a function of the space variable. In particular, we consider the case where this function is identically zero on an interval and study the dynamics of the transition layer on the interval. In this case the dynamics of the transition layer on the interval becomes so-called very slow dynamics. In order to analyze such a dynamics, we construct an attractive local invariant manifold giving the dynamics of the transition layer and we derive an equation describing the flow on the manifold. We also give applications of our results to two well known nonlinearities of bistable type.
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