Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations

2018/08/22 by Solar, Abraham
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07200

Abstract

This paper deals with the stability of semi-wavefronts to the following delay non-local monostable equation: v(t,x) = Δv(t,x) - v(t,x) + ∫_\R^dK(y)g(v(t-h,x-y))dy, x ∈ \R^d, t >0; where h>0 and d∈\Z₊. We give two general results for d≥1: on the global stability of semi-wavefronts in L^p-spaces with unbounded weights and the local stability of planar wavefronts in L^p-spaces with bounded weights. We also give a global stability result for d=1 which includes the global stability on Sobolev spaces. Here g is not assumed to be monotone and the kernel K is not assumed to be symmetric, therefore non-monotone semi-wavefronts and \it backward traveling fronts appear for which we show their stability. In particular, the global stability of critical wavefronts is stated.

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