Existence of an extinction wave in the Fisher equation with a shifting habitat

2017/02/20 by Haijun Hu, Xingfu Zou · 4 citations
Medicine · Biochemistry, Genetics and Molecular Biology · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Evolution and Genetic Dynamics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.1090/proc/13687

Abstract

This paper deals with the existence of traveling wave solutions of the Fisher equation with a shifting habitat representing a transition to a devastating environment. By constructing a pair of appropriate upper/lower solutions and using the method of monotone iteration, we prove that for any given speed of the shifting habitat edge, this reaction-diffusion equation admits a monotone traveling wave solution with the speed agreeing to the habitat shifting speed, which accounts for an extinction wave. This predicts not only how fast but also in what manner a biological species will die out in such a shifting habitat.

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