12月19号：Zhaosheng Feng：Chaotic Vibration of the Wave Equation with a van der Pol Boundary Condition

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

报告人：Zhaosheng Feng 教授

主持人：陈勇

报告时间：2016年12月19号 15:00-16:00

报告地点：中北校区理科大楼B1102

报告人简介：

冯兆生，美国德克萨斯大学(University of Texas-Rio Grande Valley)理学院数学系任终身教授、博导，主要研究方向有非线性微分方程, 动力系统, 数学物理问题, 应用分析和生物数学等。目前在数学、物理和控制工程学术刊物上共发表学术论文150余篇，近年在北美出版编辑六本英文著作/论文集，曾任第五届国际动力系统及微分方程学术大会组委会主席。目前任六个国际SCI杂志的编委，2015年获得德克萨斯大学年度杰出科研成就奖。

报告摘要：

In this talk, we consider the one-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. Since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterations, the problem is reduced to a discrete iteration problem. Following Devaney’s definition of chaos, we say that the PDE system is chaotic if the corresponding mapping is chaotic as an interval map. 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.