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

Chueh Hsin Chang, Cheng Hsiung Hsu, Tzi Sheng Yang

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
文章編號70
期刊Zeitschrift fur Angewandte Mathematik und Physik
71
發行號2
DOIs
出版狀態已出版 - 1 4月 2020

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