学术报告:2018年6月11日上午10:00点,Zhaosheng Feng 教授,University of Texas-Rio Grande Valley

发布时间:2018-06-04浏览次数:13

东南大学数学学院邀请专家申请表

  

报告人

Zhaosheng Feng

单位

University of Texas-Rio Grande Valley

报告题目

Chaotic   Vibration of the Wave Equation with a van der Pol Boundary Condition

  

报告时间

611日上午10:00

地点

数学学院第一报告厅

邀请人

虞文武教授

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 completely depends 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.

  

报告人简介

冯兆生,男,现为美国德克萨斯大学大河谷分校(University of   Texas-Rio Grande Valley)理学院数学系终身教授、博导。主要研究方向有非线性分析,混沌动力系统,微分方程及应用,数学物理问题,生物数学何数值模拟等。目前在美国、英国等国家的数学和物理学术刊物上共发表学术论文162,其中被SCI/SCI-E检索的论文近130余篇。近年在北美编辑出版6本英文著作和大会论文集,曾应邀担任十八个国际数学会议学术委员和组委会委员,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6个国际SCI杂志的编委和主编。