期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 280, 期 -, 页码 38-43出版社
ELSEVIER
DOI: 10.1016/j.physd.2014.04.010
关键词
Reaction-diffusion equation; Front propagation; Cut-offs; Variational principles
资金
- Fondecyt (Chile) [1100679, 1120836]
- Iniciativa Cientifica Milenio, ICM (Chile), through the Millenium Nucleus [RC120002]
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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