2013 Fiscal Year Final Research Report
Three-dimensional cylindrically non-symmetric traveling fronts in reaction-diffusion equations
| Project/Area Number |
23540235
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Okayama University (2013)
Tokyo Institute of Technology (2011-2012) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 進行波 / 多次元 / 反応拡散方程式 / 非対称 |
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| Research Abstract |
The results are as follows. (1) We proved N-dimensional pyramidal traveling fronts in the Allen-Cahn (Nagumo) equation.(2) We consider the Allen-Cahn (Nagumo) equation in the three-dimensional space, and proved the existence and stability of cylindrically non-symmetric traveling fronts. The cross sections of these traveling fronts are smooth convex shapes, say, ellipses. (3) We prove the existence of N-dimensional pyramidal traveling fronts in competition-diffusion systems. (4) We prove the non-existence of localized traveling spots with non-zero speed in a single reaction-diffusion equation under some condition.
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Research Products
(24 results)
