学术报告报告题目：Chaotic Vibration of the Wave Equation on a Rectangular Domain with a van der Pol Boundary Regulation and Energy Pumping
报 告人：Goong Chen教授
报告时间：2023年6月11日(星期日)上午10：00-11:30
报告地点：数学学院4318会议室
邀 请人：杨启贵教授
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数学学院
2023年6月9日
报告摘要：In this talk, we develop the plane wave propagation method to study the nonlinear wave propagation on a 2D rectangular domain where the boundary conditions on the four sides contain a van der Pol boundary regulation, energy pumping, and homogeneous Dirichlet and Neumann conservative types.The plane wave propagation allows the factorization of the 2D wave equation into the product of two 1D wave equations. Therefore, we can use the laws of reflection on each side of the rectangle to determine how waves propagate inside the rectangular domain and be continued indefinitely timewise. Other findings have shown that chaotic vibrations occur when the parameters fall within a certain range. But when the parameters fall outside a certain range, then there can be multiple solutions, or just be regular non-chaotic vibrations. In fact, the directions of wave propagations will play an extremely important role in the vibration analysis. The developed mathods can be applied, in principle, to problems in higher imensional rectangular domains. The speaker will also point out a number of open questions for further study.
报告人简介：Goong Chen is Professor of Mathematics and Aerospace Engineering. He has research interests in many areas of applied and computational mathematics: control theory for partial differential equations (PDEs), boundary element methods and numerical solutions of PDEs, engineering mechanics, chaotic dynamics, quantum computation, chemical physics and quantum mechanics. He has written over one hundred seventy papers, seven advanced texts/monographs, and co-edited four books. He is Editor-in-Chief of the Journal of Mathematical Analysis and Applications, and has served as the Editor-in-Chief of the Chapman & Hall/CRC Press Applied Mathematics and Nonlinear Science Series (2002-2011), and as Associate Editor for several other editorial boards, including the SIAM Journal on Control and Optimization, the International Journal on Quantum Information, Physica Scripta, and the Electronic Journal of Differential Equations. He is also a co-holder of a U.S. Patent on certain quantum circuit design for quantum computing. He has graduated a total of 21 PhD students.