报告人：黎定仕 副教授（西南交通大学）

报告题目：Random attractors for fractional stochastic reaction-diffusion equations on  $\R^n$

报告摘要：In this talk, we investigate the regularity of random attractors for  the   non-autonomous non-local fractional  stochastic reaction-diffusion equations  in $H^s(\R^n)$ with $s\in (0,1)$. We prove the existence and uniqueness of  the tempered random attractor that  is compact in $H^s(\R^n)$ and attracts all tempered random  subsets of $L^2(\R^n)$ with respect to the norm of $H^s(\R^n)$. The main difficulty is to show  the pullback asymptotic compactness of solutions in $H^s(\R^n)$ due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

报告人简介：黎定仕，副教授.发表SCI论文多篇，其中包括J. Differential Equation, Discrete Contin. Dyn. Syst.-A.,Discrete Contin. Dyn. syst.-B,J.Math.Phys.等国际专业刊物.

报告时间：2019年10月18日（星期五）上午10:30-12:30

报告地点：科技楼南楼602室