Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

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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Additional Information

Fumioki Asakura
Affiliation: Department of Asset Management, Osaka Electro-Communication University, Neyagawa, Osaka, Japan

Andrea Corli
Affiliation: Department of Mathematics, University of Ferrara, Ferrara, Italy

DOI: https://doi.org/10.1090/S0033-569X-2012-01318-4
Received by editor(s): April 28, 2011
Published electronically: October 2, 2012
Article copyright: © Copyright 2012 Brown University

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