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

Coupled reaction-diffusion equations on adjacent domains