The semigroup generated by a Temple class system with non-convex flux function

Abstract

We consider the Cauchy problem for a nonlinear $n \times n$ system of conservation laws of Temple class, i.e., with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.