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Ergodicity of transition semigroups for stochastic fast diffusion equations. (English) Zbl 1286.60067
Summary: 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.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
47D07 Markov semigroups and applications to diffusion processes
60J35 Transition functions, generators and resolvents
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