Granular media equation with double-well external landscape: limiting steady state

In this paper, we give a simple condition on the initial state of the granular media equation whichensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. To doso, we use functional inequalities, Laplace method and McKean-Vlasov diffusion (which corresponds to theprobabilistic interpretation of the granular media equation).