Global existence of solutions by path decomposition for a model of multiphase flow

Abstract

We consider a strictly hyperbolic system of three conservation laws, in one space dimension. The system is a simple model for a fluid flow undergoing liquid-vapor phase transitions. We prove, by a front-tracking algorithm, that weak solutions exist for all times under a condition on the (large) variation of the initial data. An original issue is the control of interactions by means of decompositions of shock waves into paths.