Coupled reaction-diffusion equations on adjacent domains

2019/03/27 by Berestycki, Henri, Rossi, Luca, Tellini, Andrea · 1 citation
#35B40 #35K40 #35K45 #35K57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.11717

Abstract

We consider a reaction-diffusion system for two densities lying in adjacent domains of ℝ^N. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two densities are considered, and an exchange occurs through the separating boundary. We study the long-time behavior of the solution, and, when it converges to a positive steady state, we prove the existence of an asymptotic speed of propagation in some specific directions. Moreover, we determine how such a speed qualitatively depends with respect to several parameters appearing in the model. In the case N=2, we compare such properties to those studied in [6-9] for a model with a line representing a road of fast diffusion at the boundary of a half-plane, which can be seen as a singular limit of the problem studied here.

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