We prove the existence of an invariant measure [mu] for the transition semigroup Pt associated with the fast diffusion porous media equation in a bounded domain , perturbed by a Gaussian noise. The Kolmogorov infinitesimal generator N of Pt in is characterized as the closure of a second-order...

We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping.

We prove, using coupling arguments, exponential convergence to equilibrium for reaction-diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.