R. Esposito, Y. Guo, R. Marra
Stability of the Front under a Vlasov-Fokker-Planck Dynamics
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ABSTRACT.  We consider a kinetic model for a system of two species of particles interacting through a long 
range repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov-Fokker-Plank equations. The important front solution, which represents the phase transition, is a one-dimensional stationary solution on the real line with given asymptotic values at infinity. We prove the asymptotic stability of the front for small symmetric perturbations.