# 2007 DiPerna Lectures

*The 2007 DiPerna Memorial Lecture will be delivered by Yuxi Zheng, Penn State, on January 25.*

Department of Mathematics, University of California, Berkeley, presents

The DiPerna Memorial Lecture 2007

**Yuxi Zheng**

Penn State

Thursday, January 25, 4 p.m.

60 Evans

**Multidimensional systems of conservation laws**

Systems of conservation laws are the physical laws of conservation of mass, momentum, and energy in the form of hyperbolic partial differential equations for modeling ideal gases, formulated primarily by L. Euler around 1776. In one space dimension, the existence and uniqueness of a solution have been established for the Cauchy problem to the primary systems of conservation laws provided that the initial data are small perturbations of constant states. While investigation remains strong in the direction for handling large data, pioneered by DiPerna, research on multidimensional systems has seen remarkable achievements in recent years as well. I plan to report these achievements, including shock reflection on a wedge and Riemann problems in two space dimensions, in addition to the state of the art large scale numerical simulations and sophisticated physical experiments.

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