报告题目：Multidimensional Riemann Problems - Transonic Shock Waves and Free Boundary Problems

报告时间：2023-12-08  16:00-17:00

报 告 人 ：Prof. Gui-Qiang G. Chen , University of Oxford

腾讯会议ID：991-598-142

Abstract：

The Riemann problem, originally proposed by Bernhard Riemann in 1860, marked the initiation of the mathematical analysis of discontinuous solutions for the one-dimensional isentropic Euler equations in gas dynamics. The first general solution to the Riemann problem for one-dimensional hyperbolic systems of conservation laws was provided by Peter Lax in 1957, laying the foundation for the one-dimensional theory of hyperbolic systems. While the one-dimensional Riemann solutions (and even more general entropy solutions) have been extensively studied, their multidimensional counterparts present more intricate global configurations and structures. The solvability of multidimensional Riemann solutions remains truly challenging and wide open in mathematics. This talk will discuss recent developments in the rigorous analysis of two-dimensional Riemann problems, specifically those involving transonic shock waves and free boundary problems, through several prototypes of hyperbolic systems of conservation laws and related nonlinear PDEs. The main focus will be on global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, with emphasis on uncovering the global configurations and structures of these solutions. Some further developments, perspectives, and open problems in this direction will be also addressed.

About the Speaker：

Professor Gui-Qiang G. Chen holds the position of Statutory Professor in the Analysis of Partial Differential Equations at the University of Oxford, where he also serves as the Director of the Oxford Centre for Nonlinear Partial Differential Equations (OxPDE) at the Mathematical Institute. Additionally, he is a Professorial Fellow of Keble College, University of Oxford. His primary research areas encompass Partial Differential Equations (PDEs), Nonlinear Analysis, and their applications to various fields within Mathematics and Science. He has made significant contributions to many fundamental research areas, including Nonlinear Hyperbolic Systems of Conservation Laws, Nonlinear PDEs of Mixed Type, Nonlinear Waves, Free Boundary Problems, Geometric Analysis, Measure-Theoretical Analysis, Weak Convergence Methods, Entropy Analysis, Stochastic PDEs, and Numerical Analysis.

Throughout his distinguished career, Professor Gui-Qiang G. Chen has authored more than 200 original research papers and over 10 research books. He holds prestigious memberships in academic societies, including being a Member of the Academia Europaea, Fellow of the European Academy of Sciences, Fellow of the American Mathematical Society, and Fellow of the Society of Industrial and Applied Mathematics. He also received many other honors and awards including the 2011 SIAG/Analysis of Partial Differential Equations Prize, Royal Society Wolfson Research Merit Award, Alexander von Humboldt Foundation Fellow, Alfred P. Sloan Foundation Fellow, and the Chinese National Natural Science Prize. Moreover, he has played editorial roles internationally, serving particularly as the Editor-in-Chief of “Acta Mathematica Scientia” and Associate Editor-in-Chief of “Science China Mathematics”, among our Chinese journals.