Systems of Conservation Equations with a Convex Extension

Abstract

We discuss first-order systems of nonlinear conservation laws which have as a consequence an additional conservation law. We show that if the additional conserved quantity is a convex function of the original ones, the original system can be put into symmetric hyperbolic form. Next we derive an entropy inequality, which has also been suggested by I. Kruzhkov, for discontinuous solutions of the given system of conservation laws.