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

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Abstract

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.

Original languageEnglish
Pages (from-to)1976-1984
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume241
Issue number22
DOIs
Publication statusPublished - 15 Nov 2012

Keywords

  • Reaction-diffusion equations
  • Front propagation
  • Cut-offs
  • Geometric desingularization
  • Maxwell point
  • SINGULAR PERTURBATION-THEORY
  • REACTION-DIFFUSION EQUATIONS
  • SPEED

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