  In this paper we study the problem of the global existence (in time) of weak,
entropic solutions to a system of three hyperbolic conservation laws, in one
space dimension, for large initial data. The system models the dynamics of
phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase
interfaces are represented as stationary contact discontinuities. We focus on
the persistence of solutions consisting in three bulk phases separated by two
interfaces. Under some stability conditions on the phase configuration and by a
suitable front tracking algorithm we show that, if the BV-norm of the initial
data is less than an explicit (large) threshold, then the Cauchy problem has
global solutions.
