Wave propagation and its stability for a class of discrete diffusion systems

Zhixian Yu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper is devoted to investigating the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the techniques of weighted energy method and the comparison principle, we show that all solutions of the Cauchy problem for the discrete diffusive systems converge exponentially to the traveling wave fronts when the initial perturbations around the wave fronts lie in a suitable weighted Sobolev space. Our main results can be extended to more general discrete diffusive systems. We also apply them to the discrete epidemic model with the Holling-II-type and Richer-type effects.

Original languageEnglish
Article number194
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume71
Issue number6
DOIs
StatePublished - 1 Dec 2020

Keywords

  • Comparison principle
  • Exponential stability
  • Super- and subsolutions
  • Traveling wave fronts
  • Weighted energy estimate

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