【廿周年院庆学术报告72】 · 【和山数学论坛第365期】

一、报告题目：Existence and stability of random attractors for 3D BBM equations driven by nonlinear noise

二、报告人：陈鹏玉 教授

三、时 间：2023年4月26日(周三)上午10:00---11:00

四、地 点：闻理园A4-218

报告摘要： In this talk I will introduce our recent work on  the long time behavior of the solutions of the non-autonomous Benjamin-Bona-Mahony equation driven by nonlinear colored noise with continuous coefficients defined on three-dimensional unbounded channels. The solutions of the equation are not unique and hence generate a multivaluednon-autonomous random dynamical system. We first prove the measurability of the multivalued random system bythe idea of weak upper semicontinuity of solutions, and then establish the existence and uniqueness of tempered pullback random attractors based on the pullback asymptotic compactness of solutions. The difficulty of the non-compactness of Sobolev embeddings on unbounded domains is overcome by the methods of the spectral decomposition inside bounded domains as well as the uniform tail-estimates of solutions outside bounded domains. Furthermore, the backward compactness and asymptotically autonomous robustness of pullback random attractors of non-autonomous Benjamin-Bona-Mahony equations driven by nonlinear colored noise defined on 3D unbounded channels has also been established.

报告人简介：陈鹏玉, 理学博士，西北师范大学数学与统计学院教授，兼任美国《Math Review》和德国《Zentralblatt MATH》评论员。 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，特别关注(随机)非局部发展方程的适定性与解的渐近行为，在国际著名数学刊物Mathematische Annalen、Journal of Geometric Analysis等上发表学术论文50余篇。主持国家自然科学基金2项，甘肃省杰出青年基金和甘肃省自然科学基金重点项目各1项。研究成果获甘肃省自然科学奖二等奖和三等奖各1项。

         欢迎广大师生参加！ 联系人：马中新。