Title: Multidimensional Conservation Laws - More Questions than Answers
Speaker: Professor Barbara Lee Keyfitz
Speaker Info: Fields Institute and University of Houston
The analysis of quasilinear hyperbolic partial differential equations presents a number of challenges. Although equations of this type are important in a number of applications, ranging from high-speed aerodynamics, through magnetohydrodynamics, to multiphase flows important in industrial technology, there is little theory against which even to check the reliability of numerical simulations.Date: Friday, January 19, 2007
Development of a theory for conservation laws in a single space variable has led to remarkable advances in analysis, including the theory of compensated compactness and the study of novel function spaces. Recently, a number of groups have begun to approach multidimensional systems via self-similar solutions.
In this talk, I will give some history of the development of conservation law theory, including an indication of why the applications are important. I will describe some of the recent results on self-similar solutions, and the interesting results in analysis that they involve. Finally, I will outline some of the paradoxical questions that remain.