Hyperbolic conservation laws. Past and future

Abstract

The field of conservation laws (quasilinear hyperbolic partial differential equations) has captured the attention of mathematics researchers, computational fluid dynamicists, and modelers of physical and engineering phenomena for over 70 years. This talk will survey some of the power, and some of the limitations, of the conservation law approach to modeling. It will also expound some of the major achievements in establishing a mathematical theory, and discuss why theoretical advances have been so slow, and why so much still seems to remain out of reach. Finally,I will describe recent work of a number of people on establishing mathematical properties of shock reflection phenomena.