Title:Weak Random Attractors and Invariant Measures of Stochastic Parabolic Equations

Speaker:Bixiang Wang

Abstract:We will discuss the asymptotic behavior of the solutions of the stochastic parabolic equations with polynomial drift terms of arbitrary order driven by nonlinear noise defined on unbounded domains. We first prove the well-posedness of the equations by the Banach fixed point theorem based on pathwise uniform estimates as well as uniform estimates on average. We then define a mean random dynamical system via the solution operators and prove the existence and uniqueness of weak pullback mean random attractors when the diffusion coefficients of the noise are locally Lipschitz continuous functions. We also establish the existence of invariant measures of the equations when the diffusion coefficients are globally Lipschitz continuous. The idea of uniform estimates on the tails of solutions at far field is employed to overcome the difficulty caused by the non-compactness of usual Sobolev embedding on unbounded domains, which plays a key role for proving the tightness of probability distributions of a family of solutions in L2(Rn).

Introduction of Speaker:Bixiang Wang, Professor, Department of Mathematics, New Mexico Institute of Mining and Technology

Inviter: ZhangCHEN Professor in School of Mathematics

Time:10:00-11:00,May 25(Saturday)

14:00-15:00,May 27(Monday)

Location:Hall 1044, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University