2015/09/09 by Debora Amadori, Paolo Baiti, Amadori, Debora +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1509.02766
arxiv created 2015/09/09 · arxiv updated 2015/09/10
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.