Strong convergence of solutions to nonautonomous Kolmogorov equations

Abstract

We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on ${\mathbb{R}}^d$ which admit an evolution system of measures. It is shown that the solutions of these equations converge to constant functions as $t\to +\infty$. We further establish the uniqueness of the tight evolution system of measures and treat the case of converging coefficients.