Asymptotic analysis and homogenization of invariant measures

Abstract

In this paper, we study limiting behavior of the invariant measures for reaction–diffusion equations in the whole space [Formula: see text] with regular and singular perturbations. In the regular case, we show the convergence of the unique stationary solution of [Formula: see text] to a stationary solution of the limiting equation [Formula: see text]. We also consider the asymptotic behavior of the stationary solution under the perturbations of spectrum. Finally, for the singular perturbation of homogenization type, we show the weak convergence of invariant measure to its homogenized limit.