Traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions

Chueh Hsin Chang, Cheng Hsiung Hsu, Tzi Sheng Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The purpose of this work is to investigate the existence and stability of monostable traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions. We first establish an innovative lemma for the existence of positive solutions to a system of linear inequalities. By this lemma, we can construct a pair of sub-super-solutions and derive the existence result by applying the technique of monotone iteration method. It is found that if the ratio of the diffusive rate of the species without nonlocal interactions to that of the other species is not greater than a specific value, then the minimal wave speed of the wavefronts is linearly determined. Moreover, by the spectral analysis of the linearized operators, we show that the traveling wavefronts are essentially unstable in the space of uniformly continuous functions. However, if the initial perturbations of the traveling wavefronts belong to certain exponential weighted spaces, then we prove that the traveling wavefronts with noncritical wave speed are asymptotically stable in the exponential weighted spaces.

Original languageEnglish
Article number70
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume71
Issue number2
DOIs
StatePublished - 1 Apr 2020

Keywords

  • Essential spectrum
  • Exponential weighted space
  • Monotone system
  • Normal spectrum
  • Positive solutions of linear inequalities
  • Super- and subsolutions

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