Hypercontractivity for space–time white noise driven SPDEs with reflection

Abstract

The hypercontractive property of the Markov semigroup associated with the reflected stochastic partial differential equation driven by the additive space–time white noise is mainly investigated. The main tool for its proof is the general criterion presented recently by F.-Y. Wang [29]. In particular, we obtain the hyperboundedness and the compactness of the Markov semigroup, the exponential convergences of the entropy, the exponential convergences of the Markov semigroup to its unique invariant measure in both L2 and the total variation norm.