学术报告（Goong Chen 6.14）

简介：

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 dimensional rectangular domains. The speaker will also point out a number of open questions for further study.

嘉宾介绍：

陈巩1972年获得中国台湾清华大学数学学士学位，1977年获得Wisconsin at Madison 大学数学博士学 位 。 1977-1978年 在 Southern Illinois University任 教 ；1978-1987年 在 Pennsylvania State University任教；1987年以来，一直在Texas A&M University in College Station, Texas 任教，分别任数学与航天工程系教授（1987-），和该校量子研究院成员（2000-）。曾访问INRIA, Centre de Recherche Mathematiques of the Universite, the Technical University of Denmark, the National University of Singapore, National Tsing Hua University。研究方向涉及应用数学和计算数学多个领域，主要包括：偏微分方程控制理论，偏微分方程的数值解和边界元法，工程力学，混沌动力学，量子计算，化学物理和量子力学。发表学术论文一百七十余篇，学术专著七本。现任国际数学期刊JMAA主编，曾任the Chapman & Hall/CRC 出版社应用数学与非线性科学序列丛书主编，还担任过 多 个 国 际 学 术 期 刊 的 编 委 ， 包 括 SIAM Journal on Control and Optimization, the International Journal on Quantum Information, Physica Scripta, the Electronic Journal of Differential Equations等。陈教授及其合作者还获得了美国量子计算某类电路设计的专利。