学术报告

报告题目：Random Attractors of Fractional Stochastic Parabolic Equations

报告人：王碧祥 教授 （新墨西哥矿业理工学院）

报告时间：2018年6月27日下午15:00-16:00

报告地点：25教14楼报告厅

报告摘要：In this talk, we discuss the long term behavior of the solutions of the non-autonomous fractional stochastic reaction-diffusion equations defined on $R^n$. We first prove the existence and uniqueness of pullback random attractors in $L^2(R^n)$ for the random dynamical system generated by the solution operators of the equations. We then establish the regularity of the random attractors in $H^s(\R^n)$ for $s\in (0,1)$ by showing these attractors are compact and pullback attract all solutions with respect to the topology of $H^s(\R^n)$. We prove the pullback asymptotic compactness of the random dynamical system in $H^s(\R^n)$ by the idea of uniform tail-estimates of the solutions on unbounded domains as well as the spectral decomposition of the solutions in bounded domains.

报告人简介：王碧祥教授现任教于美国新墨西哥理工学院数学系，主要从事偏微分方程、确定与随机动力系统及随机分析等领域的研究。在Transactions of AMS、SIAM系列杂志、JDE、JDDE等顶尖学术期刊上发表了一系列高水平的学术论文，深受到国内外同行的关注与大量引用（其中有4篇是行内高被引论文）。