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，博士，副教授，2006和2009分别毕业于中国矿业大学计算数学和应用数学专业，2012年于四川大学动力系统方向博士毕业，2012起在西南交大工作至今, 其中2014.9-2015.9访问美国杨伯翰大学.主持国家自然科学基金面上项目1项，国家自然科学基金青年项目1项，主研国家自然科学基金项目多项.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