报告人：李扬荣（西南大学）

报告题目：Numerical attractors with lower semicontinuity for porous media lattice systems

报告摘要：In this talk, we focus on discretization of global attractors for the porous media lattice system. By the implicit Euler scheme, the continuous-time model is discretized as a discrete-time porous media lattice system. We show the existence of numerical  attractors as well as  solutions  for the discrete-time system with sufficiently small step sizes, and establish the upper semi-convergence of numerical  attractors  towards  the global attractor as the step size tends to zero. We also study the numerical attractors and their approximations on the larger initial space. The second-order Taylor expansion and discretization error on the enlarged space are established to prove the upper semi-continuity of the enlarged numerical attractors in step sizes, while an upper bound of the enlarged attractors is provided to establish the lower semi-continuity in special cases. We finally establish the residual dense continuity of numerical attractors in time-sizes.

报告时间：2024年6月4日（星期二）10:00-11:30

报告地点：科技楼706室

邀请人：崔洪勇、杨爽

报告人简介：李扬荣，西南大学数学与统计学院教授，博导。96年博士毕业于南京大学，05年于北京应用物理与计算数学研究所作博士后。现任中国数学会常务理事，重庆数学会副理事长。主要研究随机或确定的无穷维动力系统，在Siam NUM, Siam JADS, J Dyn Diff Equ，J Diff Equ，Physica D, Appl Math Opt, J Appl Probab等期刊上发表论文100余篇。先后主持国家自然科学基金面上项目3项，参研教育部重点项目一项。曾获重庆市自然科学二等奖, 三等奖及重庆市优教成果二等奖各一次。