Exponential mixing for randomly forced dispersive equations
报告专家：向圣权博士（北京大学数学科学学院）
报告时间：2025年4月3日（周四）下午4:00-5:00
报告地点：国家天元数学西南中心516报告厅
报告摘要：We explore the statistical properties of dispersive equations. This study highlights the role of control properties and nonlinear smoothing in deterministic models to the ergodicity of random dynamical systems. We begin by establishing a new criterion for exponential mixing and large deviations of random dynamical systems. This criterion is then applied to randomly forced nonlinear wave equations and nonlinear Schrödinger equations with degenerate damping, critical nonlinearity, and physically localized noise. The verification of this criterion is naturally linked to topics in deterministic systems, such as exponential asymptotic compactness in dynamical systems, global stability/stabilization of the locally damped equations, and the controllability properties.
专家简介：向圣权，北京大学数学科学学院助理教授。2015年获北京大学学士学位，2017年获巴黎高等师范学院硕士学位，2019年获法国索邦大学博士学位。其主要研究方向为偏微分方程控制、随机动力系统。
邀请人：张旭
