Entropy Solution for a Hyperbolic Equation

Abstract

Nonlinear hyperbolic systems of conservation laws play a central role in Science and Engineering, and their mathematical theory as well as their numerical approximation have made recent significative progress. This paper deals with the existence and uniqueness of an entropy solution of the Cauchy problem for the quasi-linear equation $u-t+a(f(u){)}_x=0$ in one space dimension, where $a$ is a non-smooth coefficient.