报告一题目：Bounded Wave Solutions ofKdV-Burgers-type Equations

报告人：冯兆生教授（美国德克萨斯大学）

报告时间：2021年8月26日下午15:00-16:00

报告地点：复杂系统研究所报告厅

报告摘要：In this talk, we are concerned with bounded wave solutions of a class of the KdV-Burgers-type systems by starting with Burgers-type equations, and then focus on the higher-order KdV-Burgers equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. By applying the associated equivalence algebra, the Abel operator and the Lie symmetry, explicit-implicit bounded wave solutions and asymptotic behaviors are presented.

报告二题目：Chaotic properties of wave equations with van der Pol conditions  

报告人：冯兆生教授（美国德克萨斯大学）

报告时间：2021年8月26日下午16:00-17:00

报告地点：复杂系统研究所报告厅

报告摘要：In this talk, we consider the one-, two- and three-dimensional wave equation with van der Pol type conditions. The symmetric nonlinearities of van der Pol type are proposed at the two boundary endpoints, which can cause the energy of the system to rise and fall within certain bounds. Qualitative and numerical techniques are developed to tackle the cubic nonlinearities and the chaotic regime is determined. Numerical simulations and visualizations of chaotic vibrations are illustrated by computer graphics.

报告人简介：冯兆生，美国德克萨斯大学大河谷分校(University of Texas-RGV)数学与统计学院的终身教授，主要研究方向有非线性分析，分支和混沌理论，数学物理问题，数值计算和生物数学等。曾于2015和2021年两次获得德克萨斯大学年度杰出成就奖