Department of Mathematics

Speaker: Zhouping Xin
Title: Mixed Type Equations and Transonic Shocks
Affiliation: The Chinese University of Hong Kong
Date: Friday, October 30, 2009
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. The mathematical theory of systems of multi-dimensional hyperbolic conservations remains a great challenge to the field of nonlinear partial differential eqations. One of the main difficulties in dealing with such a system is the system is mixed type so that the classical approaches fail to yield the global well-posedness theory. This is so even for the important compressible Euler systems in gas dynamics. In this talk, I will illustrate these by the example of steady compressible flows in multi-dimensional ducts with varaible sections. In particular, I will discuss some recent results on the transonic shock problem in a de Laval nozzle due to Courant-Friedrichs.