Bio

Professor Song Jiang is a member of the Chinese Academy of Science, a research fellow of the Institute of Applied Physics and Computational Mathematics in Beijing, and a famous applied mathematician. He majors in the mathematical theories, numerical methods and applications of compressible fluid mechanics. He has made a series of achievements in many fields, such as the well-posedness theory of the compressible Navier-Stokes equation, Reyleigh-Taylor instability of fluid and magnetofluid, and mathematical analysis for small Mach limit. In the application, Professor Jiang and his colleagues have put forward many new practical algorithms, like the whole ALE and local Euler coupling method, to overcome the computational difficulties in the numerical simulation of weapons' physical properties, and developed a numerical simulation software platform for heavy weapons. Professor Jiang has won many awards, including the second prize of China's State Natural Science Award, the first prize of Military Progress Award in Science and Technology, the Chinese Youth Prize for Science and Technology and the Qiushi Youth Award.

Abstract

Partial differentials equations models are ubiquitous in diverse fields such as science and engineering, economy, and national defense. The analysis and numerical simulation of these PDE models are crucial to the development of these fields. With the rapid advances of computer technology and computational methods, numerical solutions of PDEs, i.e., scientific computing, have become an important research tool, parallel to analysis and laboratory experiments in some sense. In this talk, I will give a brief survey of various applications of PDEs in science and engineering, current hot topics in terms of their analysis and numerical simulations, and challenges and potential solutions.