报告题目：Multivalued and finite-dimensional random dynamics of critically

nonlinear BBM equations driven by colored noise

报告人：王仁海教授(贵州师范大学)

报告时间：2025年12月14日星期日10：30—11：30

报告地点：数理楼145

报告摘要：We consider the generalized Benjamin-Bona-Mahony equation driven by colored noise on an unbounded domain that supports the Poincare inequality. The drift term exhibits a critically polynomial growth rate, while the diffusion diffusion term is non-Lipschitz. We first prove the existence of a global weak solution by combining a Galerkin scheme with an unbounded-domain truncation technique. We then establish an H^1-energy-balance equality that holds for every weak solution with minimum regularity, independently of the Galerkin approximation procedure. We construct a multivalued non-autonomous random dynamical system, and show that it possesses a unique weakly tempered random attractor. We also derive a unified criterion to estimate the uniform upper bounds of fractal dimension of random invariant sets of non-autonomous random dynamical systems. This criterion is used to obtain a uniform upper bound of fractal dimension of the random attractor of the random BBM equation.

报告人简介：王仁海，贵州师范大学校聘教授、博士生导师，西南大学与美国New Mexico Institute of Mining and Technology联合培养博士，北京应用物理与计算数学研究博士后，长期从事确定和随机无穷维动力系统理论及应用的研究。主持国家自然科学基金青年项目和数学天元项目以及中国博士后科学基金特别资助，面上资助和优秀学术出版资助，获重庆市优秀博士学位论文称号，入选贵州省科学技术协会首届青年人才托举工程和贵州省教育厅青年拔尖科技人才项目，其论文发表于《Math. Ann.》、《Math. Mod. Meth. Appl. Sci.》、《Int. Math Res. Notice》与《SIAM J. Math. Anal.》等刊物。