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

作　　者：Debora AMADORI Paolo BAITI Andrea CORLI Edda DAL SANTO 

机构地区：[1]Department of Engineering and Computer Science and Mathematics, University of L'Aquila [2]Department of Mathematics and Computer Science, University of Udine [3]Department of Mathematics and Computer Science, University of Ferrara

出　　处：《Acta Mathematica Scientia》2015年第4期832-854,共23页数学物理学报（B辑英文版）

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.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 trackingalgorithm 

分 类 号：O175.27[理学—数学] O359[理学—基础数学]