A Contractive Metric for Systems of Conservation Laws with Coinciding Shock and Rarefaction Curves

We introduce two algorithms for the construction of weak, entropy-admissible solutions to a class of systems of conservation laws with coinciding shock and rarefaction curves. Global existence, uniqueness, and continuous dependence are proved for all solutions obtained by our constructive procedure. The generated semigroup is contractive with respect to a Riemann-type metric, defined in terms of Glimm′s wave interaction functional, equivalent to the usual 1 distance.