Report title: Partial Differential Equations: Function, Analysis and Numerical Solution

Reporter: Jiang Song, researcher, Beijing Institute of Applied Physics and Computational Mathematics

Report time: September 27, 2020 9:00

Location: Lecture Hall on the second floor of the School of Mathematics

School contact: Zhang Ran zhangran@jlu.edu.cn

Report summary:

      Many mathematical models of partial differential equations have been proposed in the fields of science and engineering technology, economy and national defense construction. The theoretical analysis and numerical solution of these models play a very important role in promoting the development of related fields. In particular, with the rapid development of computer technology and calculation methods, the numerical solution of differential equations (that is, scientific and engineering calculations) has become an important research method for scientific and technological innovation along with theoretical research and experimental research. This report will combine specific examples to briefly introduce the role of partial differential equations in the fields of science and engineering, its mathematical theory and numerical solution research hot issues, challenges and possible solutions.

Brief introduction of the speaker:

　　 Jiang Song, an applied mathematician, graduated from the Department of Mathematics of Sichuan University in 1982, received a master's degree from Xi'an Jiaotong University in 1984, and a doctorate degree from the University of Bonn, Germany in 1988. Elected as an academician of the Chinese Academy of Sciences in 2015. Researcher and Secretary of the Party Committee of Beijing Institute of Applied Physics and Computational Mathematics. Mainly engaged in compressible fluid mechanics mathematical theory, calculation method and application research. In theory, for any adiabatic exponent γ>1, and collaborators proved the existence of weak solutions to the three-dimensional steady and compressible Navier-Stokes (NS) equations with large external forces, and the high-dimensional unsteady NS equations with large initial values. The overall existence of axisymmetric solutions. In terms of application, in view of the calculation difficulties of large multi-medium deformation and grid distortion in the numerical simulation of weapon physics, together with colleagues, we proposed several practical new algorithms (such as the overall ALE local Euler natural coupling method), and developed major weapon models. Numerical simulation software platform. He has won the second prize of National Natural Science Award, the first prize of Military Science and Technology Progress Award, the China Youth Science and Technology Award, and the Outstanding Youth Award for Seeking Truth.