Traveling fronts in space-time periodic media

2016/09/06 by Nadin, Grégoire · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1609.01431

Abstract

This paper is concerned with the existence of pulsating traveling fronts for the equation: ∂_t u - ∇ ⋅ (A(t, x)∇ u) + q(t, x) ⋅ ∇ u = f (t, x, u), (1) where the diffusion matrix A, the advection term q and the reaction term f are periodic in t and x. We prove that there exist some speeds c^* and c^** such that there exists a pulsating traveling front of speed c for all c≥ c^** and that there exists no such front of speed c

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