coupling of lighthill–whitham–richards and phase transition models

This paper deals with coupling conditions between the classical Lighthill-Whitham-Richards model and a phase transition model. We propose two different definitions of solution at the interface between the two models. The first one corresponds to maximize the flux passing through the interface, while the second one imposes an additional constraint on the flux. We prove existence of solutions to the Cauchy problem with arbitrary initial data of bounded variation, by means of the wave-front tracking technique. © 2013 World Scientific Publishing Company.