中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 陈鹏玉 教授（西北师范大学）
Inviter: 张志涛
Language: Chinese
Title: Random dynamics of Benjamin-Bona-Mahony equations driven by nonlinear noise
Time & Venue：2026年7月1日（星期三） 10:00-11:00 南楼N820
Abstract: In this talk, I will introduce our recent work on the existence and upper semi-continuity of pullback random attractors for non-autonomous Benjamin-Bona-Mahony equations driven by nonlinear colored noise defined on 3D unbounded channels. We first prove the existence, uniqueness, and backward compactness of a special kind of pullback random attractor by the methods of spectral decomposition inside bounded domains as well as the uniform tail-estimates of solutions outside bounded domains over the infinite time interval in order to surmount the difficulties caused by lack of compact Sobolev embedding on unbounded domains and weak dissipative structure of the equation. The measurability of such an attractor is proven by showing that the defined two kinds of attractors with respect to two different universes are equal. Then, the asymptotically autonomous upper semi-continuity of the attractors is investigated by assuming that the time-dependent external forcing term converges to the time-independent external force as the time-parameter tends to negative infinity. At last, the upper semi-continuity of random attractors for non-autonomous Benjamin-Bona-Mahony equations with nonlinear colored noise and time-delay as time delay approaches zero is established.
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