应我校数学科学学院邀请，安徽大学的李丹教授将于2023年7月21日为我校师生讲学。欢迎全校相关教师、博士生、硕士生参加!

报告题目：随机切换系统周期概率测度解的存在性

报告人：李丹 教授

报告人单位：安徽大学

时 间：2023年7月21日（周五）9：00

报告地点：数学科学学院7楼报告厅

主办单位：重点建设与发展工作处、数学科学学院

李丹教授简介：理学博士。主要从事生物数学中种群与传染病系统随机方法建模和动力学理论分析研究。作为项目负责人承担国家自然科学基金项目2项，作为主要参加者参与国家自然科学基金面上项目1项，在包括Journal of Differential Equations，Discrete and Continuous Dynamical Systems，Bulletin of Mathematical Biology等应用数学领域学术期刊上发表论文数篇。

报告摘要：In this talk, we will discuss the existence of periodic probability measure solutions to the Fokker-Planck equation associated to a periodic stochastic differential equation with random switching and irregular coefficients. The coefficients are driven by a continuous-time Markov chain with the transition rate matrix being time periodic and depending on the state variables of the system. For cooperative weakly coupled parabolic systems, the results on the principal eigenvalue and principal eigenfunction, the locally uniform Holder estimates of solutions and Harnack inequality, are extended. Based on these results, we establish a periodic Lyapunov condition ensuring the existence of periodic probability measure solutions to the Fokker-Planck equation in both non-degenerate and degenerate cases.

欢迎各位老师同学届时参加！