Uniqueness, regularity and behaviour in time of the solutions to nonlinear anisotropic parabolic equations

Abstract

In this paper we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness results. We indagate on the behavior in time of the solutions with a particular attention to the autonomous case f(x, t) = f(x).