@article{ECP1643,
author = {Wei Liu and Jonas Toelle},
title = {Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {stochastic evolution equation; invariant measure; dissipative; \$p\$-Laplace equation; fast diffusion equation},
abstract = {In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].},
pages = {no. 40, 447-457},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1643},
url = {http://ecp.ejpecp.org/article/view/1643}}