The Cauchy problem for a class of $2\times 2$ hyperbolic systems of conservation laws with unbounded propagation speed

Abstract

This paper shows the existence of time-global continuous characteristic solutions of the Cauchy problem for a class of $2 \times 2$ weakly hyperbolic systems of conservation laws in one space dimension with possibly unbounded initial propagation speed, and gives a condition on the growth of the initial propagation speed necessary and sufficient for the uniqueness of continuous solutions.