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，贵州师范大学

邀 请 人：刘辉

报告时间：2026年05月16日（星期六）16:10-16:50

报告地点：7JC214

报告摘要：We consider a generalized Benjamin-Bona-Mahony equation driven by colored noise on an unbounded domain that supports the Poincar'e inequality. The drift term exhibits critically polynomial growth, while the diffusion term is non-Lipschitz. By combining a Galerkin scheme with an unbounded-domain truncation technique, we prove the existence of global weak solutions. We establish an H1-energy-balance equality that holds for arbitrary selections of weak solutions. We construct a multivalued non-autonomous random dynamical system and show that it possesses a unique weakly tempered random attractor. We derive an abstract criterion for estimating uniform upper bounds on the fractal dimension of random invariant sets of non-autonomous random dynamical systems. This criterion can be applied to estimate uniform upper bounds on the fractal dimension of random attractors for both parabolic- and hyperbolic-type PDEs driven by non-autonomous and random/stochastic forcing.

报告人简历：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，长期从事确定性和随机无穷维动力系统及偏微分方程理论与应用的研究。主持国家自然科学基金项目2项、中国博士后科学基金项目3项，入选贵州省高层次人才培养支持工程（青年拔尖人才）和贵州省科学技术协会青年人才托举工程。相关研究成果表于《Math. Ann.》、《Math. Mod. Meth. Appl. Sci.》、《Int. Math Res. Notice》、《SIAM J. Math. Anal.》与《J. Differ. Equ.》等刊物。