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

Asakura, Fumioki; Corli, Andrea

doi:10.1090/S0033-569X-2012-01318-4

Authors: Fumioki Asakura and Andrea Corli
Journal: Quart. Appl. Math. 71 (2013), 135-182
MSC (2010): Primary 35L65; Secondary 35D30, 76T30
DOI: https://doi.org/10.1090/S0033-569X-2012-01318-4
Published electronically: October 2, 2012
MathSciNet review: 3075539
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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.

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