A geometric analysis of front propagation in an integrable Nagumo equation with a linear cut-off

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Popovic, Nikola^1,2 

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

[2] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3JZ, Midlothian, Scotland

关键词: Reaction-diffusion equations;    Front propagation;    Cut-offs;    Geometric desingularization;    Maxwell point;   

DOI  :  10.1016/j.physd.2011.05.007

来源: Elsevier

【 摘 要 】

We investigate the effects of a linear cut-off on front propagation in the Nagumo equation at a so-called Maxwell point, where the corresponding front solution in the absence of a cut-off is stationary. We show that the correction to the propagation speed induced by the cut-off is positive in this case; moreover, we determine the leading-order asymptotics of that correction in terms of the cut-off parameter, and we calculate explicitly the corresponding coefficient. Our analysis is based on geometric techniques from dynamical systems theory and, in particular, on the method of geometric desingularization ('blow-up'). (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free