On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment

Hu, Haijun; Yi, Taishan; Zou, Xingfu

doi:10.1090/proc/14659

On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment
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by Haijun Hu, Taishan Yi and Xingfu Zou PDF

Proc. Amer. Math. Soc. 148 (2020), 213-221 Request permission

Abstract:

We consider a generalized Fisher-KPP equation with the growth function being time and space dependent in the form of “shifting with constant speed”. The main concerns are extinction and persistence, as well as spatial-temporal dynamics. By employing a new method relating to semigroup and some subtle estimates, we not only extend the main results in Li et al. [SIAM J. Appl. Math. 74 (2014), pp. 1397-1417] to a scenario when the growth function may have no sign change, but also improve the main results there by dropping some restrictions on the initial functions.

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