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

Hu, Haijun; Zou, Xingfu

doi:10.1090/proc/13687

Existence of an extinction wave in the Fisher equation with a shifting habitat
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by Haijun Hu and Xingfu Zou PDF

Proc. Amer. Math. Soc. 145 (2017), 4763-4771 Request permission

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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