Fakult?t für Mathematik, Universit?t Bielefeld, D-33501 Bielefeld, Germany
Abstract:
In this paper, we first show the uniqueness of invariant measures for the stochastic fast diffusion equation, which follows
from an obtained new decay estimate. Then we establish the Harnack inequality for the stochastic fast diffusion equation with
nonlinear perturbation in the drift and derive the heat kernel estimate and ultrabounded property for the associated transition
semigroup. Moreover, the exponential ergodicity and the existence of a spectral gap are also investigated.