The evolution of travelling waves in the weakly hyperbolic Fisher model

David Needham, Andrew King

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper we consider an initial boundary-value problem for a weakly hyperbolic generalized Fisher equation of order p > 0. We show that for each p > 0 the large time structure of the solution involves the evolution of a propagating wavefront. However, we demonstrate that the case p = 1 is a bifurcation point in the sense that for p greater than or equal to 1 the wavefront is of reaction-diffusion type, while for 0 <p <1, then the wavefront is of reaction-relaxation type.
Original languageEnglish
Pages (from-to)1055-1088
Number of pages34
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volume458
DOIs
Publication statusPublished - 8 May 2002

Keywords

  • weakly hyperbolic Fisher model
  • reaction-relaxation waves
  • reaction-diffusion waves

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