学术报告报告题目：Asymptotic stability of evolution systems of probability measures for nonautonomous stochastic systems: Theoretical results and applications
报 告人：王仁海博士（北京应用物理与计算数学研究所）
报告时间：2022年4月29日（星期五）晚上8:00-- 9:00
报告地点：腾讯会议：561 494 519，密码：220429
邀 请人：曾才斌 副教授
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数学学院
2022年4月26日
报告摘要：The asymptotic stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this talk we initiate a program to study the asymptotic stability of evolution systems of probability measures of time inhomogeneous transition operators for nonautonomous stochastic systems. A general theoretical result on this topic is established in a Polish space by establishing some sufficient conditions which can be verified in applications. Our abstract results are applied to a stochastic lattice reaction-diffusion equation driven by a time-dependent nonlinear noise. A time-average method and a mild condition on the time-dependent diffusion function are used to prove that the limit of every evolution system of probability measures must be an evolution system of probability measures of the limiting equation. This is a joint work with Tomás Caraballo and Nguyen Huy Tuan.
报告人简介：王仁海，西南大学与美国新墨西哥理工大学的联合培养博士（导师：李扬荣教授与Bixiang Wang教授），现为北京应用物理与计算数学研究所博士后（合作导师：郭柏灵院士），主要研究方向为随机动力系统与随机微分方程。 目前，他已在Mathematische Annale, Stoch. Proc. Appl., JDE, JDDE, Nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A, DCDS-A, 中国科学数学（英文版）等期刊发表多篇学术论文。