报告题目：Upper semi-continuity of random attractors for BBM equations driven by nonlinear colored noise
报告人：陈鹏玉 教授
报告时间：2025年05月23日（星期五）上午10:00-11:00
报告地址：藕舫楼724室
主持人：吕广迎 教授
报告摘要：In this talk I will introduce our recent work on the 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.
报告人简介：陈鹏玉，西北师范大学教授、博士生导师，数学与统计学院副院长，兼任美国Math Review和德国Zentralblatt MATH评论员。2024年入选全球前2%顶尖科学家榜单，2023年入选甘肃省领军人才，2022年入选甘肃省“飞天学者”特聘计划，2021年获甘肃省杰出青年基金资助。主要从事非线性分析与随机动力系统的研究，在国际著名数学刊物Mathematische Annalen、SIAM Journal on Mathematical Analysis、Journal of Geometric Analysis、Stochastic Processes and their Applications、Discrete and Continuous Dynamical Systems、Journal of Dynamics and Differential Equations、Journal of Evolution Equations等上发表学术论文80余篇。主持国家自然科学基金3项，甘肃省杰出青年基金、甘肃省自然科学基金重点项目等科研项目近10项。研究成果获甘肃省自然科学奖二等奖、三等奖和甘肃省高等学校科技进步奖共4项。
欢迎广大师生踊跃参加！
数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2025年05月14日
