Invariant measures of fractional stochastic parabolic equations

主讲人：Bixiang Wang，新墨西哥矿业理工大学教授

时间：2019年10月14日15：00

地点：3号楼332报告厅

举办单位：数理学院

内容介绍：We will study the invariant measures of fractional stochastic parabolic equations defined on unbounded domains. The nonlinear drift term is a locally Lipschitz function with polynomial growth rate and the nonlinear diffusion term is a globally Lipschitz function with linear growth rate. We first derive the mean-square uniform estimates of solutions and then prove the tightness of probability distributions of a family of solutions in L^2 (R^n). Finally, we show the existence of invariant measures of the equation by Krylov-Bogolyubov's method. The idea of uniform estimates on the tails of solutions is employed to show the tightness of solutions in order to overcome the difficulty caused by the non-compactness of usual Sobolev embedding on unbounded domains.