We consider kinetic models undergoing phase transi- tion. We discuss the problem of finding the stable stationary solutions, by looking at the mimizers of the free energy functional for different interactions. Then, we consider a binary mixture, with repulsion between different species, described by a set of two coupled Vlasov-Fokker-Plank equations. We prove the asymptotic stability for small symmetric perturbations of the front solution, which represents the transition profi le between two co- existing phases, and we give also the rate of convergence. Extensions to the fi nite torus will be discussed.
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