报告题目：Stability Analysis of Nonlinear PDEs under Dynamic Boundary Conditions

报告人： 赵昆 教授(Tulane University)

报告时间：2023年6月27日上午10点00 分-11点00分

报告地点： 数135

报告摘要：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硕士，美国乔治亚理工学院博士，美国俄亥俄州立董事长物数学研究所博士后，曾任美国爱荷华大学数学系访问助理教授。从事流体力学，生物数学，数学物理等领域中非线性偏微分方程的定性和定量分析研究。在 ARMA，SIAM J Math Analysis，Indiana University Math J，SIAM J Applied Math，JDE，M3AS，Physica D，J Math Biology，Nonlinearity，European J Applied Math 等国际知名期刊上发表 SCI 论文 60 余篇。现担任杂志《Annals of Applied Mathematics》编委，主持完成并参与审阅多项美国自然科学基金项目。