Hysteresis rarefaction in the Riemann problem

We consider the wave equation with Preisach hysteresis and Riemann initial data as a model for wave propagation in hysteretic (e.g. elastoplastic) media. The main result consists in proving that in the convex hysteresis loop domain, there exists a unique self-similar locally Lipschitz continuous solution. In other words, smooth rarefaction waves propagate in both directions from the initial jump discontinuity.