 
Summary: Proceedings of Symposia in Applied Mathematics
Global solutions for a hyperbolic model of multiphase flow
Debora Amadori and Andrea Corli
Abstract. We study a strictly hyperbolic system of three balance laws arising
in the modelling of fluid flows, in one space dimension. The fluid is a mixture
of liquid and vapor, and pure phases may exist as well. The flow is driven by
a reaction term depending either on the deviation of the pressure p from an
equilibrium value pe and on the mass density fraction of the vapor in the fluid;
this makes possible for metastable regions to exist. A relaxation parameter is
also involved in the model.
First, for the homogeneous system, we review a result about the global
existence of weak solutions to the initialvalue problem, for initial data with
large variation. Then we focus on the inhomogeneous case. For initial data
sufficiently close to the stable liquid phase we prove, through a fractional step
algorithm, that weak global solutions still exist. At last, we study the relax
ation limit under such assumptions, and prove that the solutions previously
constructed converge to weak solutions of the homogeneous system for the
pure liquid phase.
1. Introduction
In the last years the theory of hyperbolic balance laws in one space dimen
