兰州大学“聚英萃华”萃英学院学术讲座（第三百六十一场）——ZhaoshengFeng教授

应兰州大学萃英学院、数学与统计学院邀请，美国德克萨斯大学RGV分校ZhaoshengFeng教授开设线上学术报告，欢迎广大师生参加。

报告题目：Chaotic Vibration of the Wave Equation with a van der Pol Boundary Condition

报告人：Zhaosheng Feng教授

报告时间：10月25日(周五)21:00

腾讯会议ID：774587891

报告人简介：

博士，毕业于美国德克萨斯A&M大学，现为美国德克萨斯大学RGV分校Carlos and StephanieManrique de Lara 讲席教授，2024 年获得该校Distinguished Career Award。主要研究方向是非线性分析，动力系统，分支与混沌理论，数学物理问题，数值计算和生物数学等，已经发表学术论文200 余篇。曾应邀在多个国际学术会议上做过大会报告，担任 SCI 学术期刊《Communications in Nonlinear Science and NumericalSimulation》和《Electronic Journal of Differential Equations》的主编，同时担任多个国际学术杂志的编委。

摘要：

In this talk, we consider the 2-dimensional wave equation on the unit interval [0, 1]. At the left end x = 0, an energy injecting boundary condition is posed, and at the right end, x = 1, the boundary condition is a cubic nonlinearity, which is a van der Pol type condition. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem in terms of an equivalent first order hyperbolic system and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Qualitative and numerical techniques are developed to tackle the cubic nonlinearities, and the chaotic results are established. Numerical simulations and visualizations of chaotic vibrations are illustrated by computer graphics.