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arXiv · 1903.11717

Coupled reaction-diffusion equations on adjacent domains

Henri Berestycki·Luca Rossi·Andrea Tellini
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Abstract

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. 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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Henri Berestycki, Luca Rossi, Andrea Tellini. 2019-03-27. Coupled reaction-diffusion equations on adjacent domains. https://doi.org/10.1142/s0219199725500567

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