期刊论文详细信息
PHYSICA D-NONLINEAR PHENOMENA 卷:280
Shift in the speed of reaction-diffusion equation with a cut-off: Pushed and bistable fronts
Article
Benguria, R. D.1  Depassier, M. C.1 
[1] Pontificia Univ Catolica Chile, Inst Fis, Santiago 22, Chile
关键词: Reaction-diffusion equation;    Front propagation;    Cut-offs;    Variational principles;   
DOI  :  10.1016/j.physd.2014.04.010
来源: Elsevier
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【 摘 要 】

We study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut-off. We give explicit formulas for the shift in the speed for arbitrary reaction terms f(u). The dependence of the speed shift on the cut-off parameter is a function of the front speed and profile in the absence of the cut-off. In order to determine the speed shift we solve the leading order approximation to the front profile u(z) in the neighborhood of the leading edge and use a variational principle for the speed. We apply the general formula to the Nagumo equation and recover the results which have been obtained recently by geometric analysis. The formulas given are of general validity and we also apply them to a class of reaction terms which have not been considered elsewhere. (C) 2014 Elsevier B.V. All rights reserved.

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