A hyperbolic model of two-phase flow: global solutions for large initial data

Abstract

The paper deals with a simple nonlinear hyperbolic system of conservation laws modeling the flow of an inviscid fluid. The model is given by a standard isothermal p-system of the gasdynamics, for which phase transitions of the fluid are taken into consideration via a third homogeneous equation. We focus on the case of initial data consisting of two different phases separated by an interface. By means of an adapted version of the front tracking algorithm, we prove the global-in time existence of weak entropic solutions under suitable assumptions on the (possibly large) initial data.