题目: Stability Analysis of Nonlinear PDEs under Dynamic Boundary Conditions
报告人：赵昆（美国杜兰大学）
时间：2023年6月26日下午15：00-16：00
地点：数学院203教室
邀请人：张华丽
摘要: The study of partial differential equations (PDE) on spatial domains with physical
boundaries supplemented with dynamic boundary conditions (DBC) is closely related to the
control of solutions to the models. For example, a given dynamic pressure drop at the physical
boundary, associated with a simplified fluid dynamics model, was utilized to control the blood
flow through small arteries (Canic 2003). Also, the boundary control problem of the heat
equation was studied to find the optimal heat transfer coefficient (Homberg 2013). Comparing
with extensive numerical studies, the rigorous analysis of such problems is relatively rare. In
this talk, I will present some rigorous mathematical results concerning the stability of large-data
solutions to certain nonlinear PDE models, including the 2D Boussinesq equations and a system
of hyperbolic balance laws from chemotaxis, subject to various types of dynamic boundary
conditions. These are based on a series of recent joint works with Zefu Feng (Chongqing
Normal), Rosa Fuster-Aguilera (Colorado-Boulder), Vincent Martinez (CUNY-Hunter), Jiahong
Wu (Notre Dame), Yanni Zeng (Alabama), and Min Zhang (Harbin Engineering).
报告人简介：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，美国俄亥俄州立大学生物研究所博士后，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., J. Geom. Mech., J.Math.Biol., European J.Appl.Math., Nonlinearlity等国际知名期刊上发表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。
