Asymptotic behavior in time periodic parabolic problems with unbounded coefficients

Abstract

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb{R}\times {\mathbb{R}}^d$. Our results generalize and improve asymptotic behavior results for Markov semigroups having an invariant measure. We also study spectral properties of the realization of the parabolic operator $u\mapsto \mathcal{A}(t)u-u_t$ in suitable $L^p$ spaces.