Conservation Laws With Random and Deterministic Data

Abstract

The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The introduction of randomness in any of several forms into the initial condition makes the problem even more interesting. We present a broad spectrum of results from a number of works, both deterministic and random, to provide a diverse introduction to some of the methods of analysis for conservation laws. Some of the deep theorems are applied to discrete examples and illuminated using diagrams.