# 2008 DiPerna Lectures

*The 2008 DiPerna Memorial Lecture will be delivered by Gui-Qiang Chen, Northwestern, on January 31.*

Department of Mathematics, University of California, Berkeley, presents

The DiPerna Memorial Lecture 2008

**Gui-Qiang Chen**

Northwestern University

Thursday, January 31, 4 p.m.

60 Evans

**Nonlinear Conservation Laws of Mixed Type in Mechanics and Geometry**

**Many nonlinear partial differential equations arising naturally in mechanics and geometry are of mixed type, including nonlinear conservation laws of mixed hyperbolic-parabolic type and mixed hyperbolic-elliptic type. The solution of some fundamental issues in these areas greatly requires a deep understanding of such nonlinear partial differential equations of mixed type. Important examples include nonlinear degenerate diffusion-convection equations and transonic flow equations in fluid mechanics and the Gauss-Codazzi system for isometric embedding in differential geometry. In this talk we will discuss some recent developments in the study of nonlinear conservation laws of mixed type through these examples with emphasis on identifying/developing unified mathematical approaches, ideas, and techniques to deal with the mixed-type problems. Further trends, perspectives, and open problems in this direction will be also addressed.**

*Abstract:**Refreshments will be served in 1015 Evans, 3:00-4:00pm*