报告人 ：赵昆（杜兰大学）

时间：2023年06月07日 10:00--

地址：理科楼LA106

摘要：The one-dimensional dissipative Boussinesq equations (DBE) can describe the propagation of weak tidal bores on the surface of a horizontally isotropic fluid. In this presentation, we will introduce rigorous mathematical results concerning controlled dynamics by dynamic boundary conditions, and existence/stability of traveling waves of the model. Global stability of large data solutions subject to time-dependent boundary conditions is achieved via entropy and energy methods. Existence of traveling waves is obtained by means of phase plane analysis and geometric singular perturbation. Local stability of traveling waves with arbitrary strengths is proven by spatially weighted energy methods. Numerical results on the DBE and rigorous results on a related model from chemotaxis will also be discussed. This talk is based on recent joint works with Ying Bi, Ricardo Cortez, Zefu Feng, Rosa Fuster-Aguilera, Vincent Martinez, Zhian Wang, Anita Yang, and Neng Zhu.

简介：赵昆，美国杜兰大学数学系教授，中国科学技术大学本科，美国乔治亚理工学院博士，美国俄亥俄州立老员工物研究所博士后，曾任美国爱荷华大学数学系访问助理教授。从事生物数学、流体力学、数学物理领域中非线性偏微分方程的定性和定量分析研究。在Arch. Ration. Mech. Anal.、 Indiana Univ. Math. J.、SIAM J. Math. Anal.、 Math. Models Methods Appl. Sci.、Physical D、J. Differential Equations等期刊上发表SCI论文50多篇。现担任杂志《Annals of Applied Mathematics》编委，主持完成多项美国自然科学基金项目。

邀请人：穆春来、王华桥

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