GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

doi:10.1016/S0252-9602(15)30024-2

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (4): 832-854.doi: 10.1016/S0252-9602(15)30024-2

GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

Debora AMADORI¹, Paolo BAITI², Andrea CORLI³, Edda DAL SANTO¹

收稿日期:2015-02-21 出版日期:2015-07-01 发布日期:2015-07-01

GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

Debora AMADORI¹, Paolo BAITI², Andrea CORLI³, Edda DAL SANTO¹

1. Department of Engineering and Computer Science and Mathematics, University of L'Aquila, Italy;
2. Department of Mathematics and Computer Science, University of Udine, Italy;
3. Department of Mathematics and Computer Science, University of Ferrara, Italy

Received:2015-02-21 Online:2015-07-01 Published:2015-07-01

摘要/Abstract

摘要：

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.

关键词: hyperbolic systems of conservation laws, phase transitions, wave-front tracking algorithm

Abstract:

Key words: hyperbolic systems of conservation laws, phase transitions, wave-front tracking algorithm

Debora AMADORI, Paolo BAITI, Andrea CORLI, Edda DAL SANTO. GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES[J]. 数学物理学报(英文版), 2015, 35(4): 832-854.

Debora AMADORI, Paolo BAITI, Andrea CORLI, Edda DAL SANTO. GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES[J]. Acta mathematica scientia,Series B, 2015, 35(4): 832-854.

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GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

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