2009 Fiscal Year Final Research Report
Structure of linearized eigenvalue problems associated with reaction-diffusion equations and applications
| Project/Area Number |
20740096
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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 | Waseda University |
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Principal Investigator |
WAKASA Tohru Waseda University, 理工学術院, 助教 (20454069)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 非線形現象 / パターン形成 / 反応拡散方程式 / 定常解 / 固有値問題 |
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| Research Abstract |
Some of pattern formation phenomena in nature are described by reaction-diffusion equations. In this research subject, the bistable reaction-diffusion equations describing phase transition is considered, and in particular, its linearized eigenvalue problems associated with stationary layer patterns are analyzed. The relationship between pattern of stationary solutions and those of eigenfunctions is of interest, and asymptotic formulas which provide patterns of most eigenfunctions are proved.
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