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A hyperBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

Acta Mathematica Scientia 2010年第2期30卷 391-427页

作者： Gui-Qiang G.Chen School of Mathematical Sciences,Fudan University,Shanghai 200433,China Mathematical Institute,University of Oxford,24-29 St Giles,Oxford,OX1 3LB,UK Department of Mathematics,Northwestern University,Evanston,IL 60208-2730,USA Weihua Ruan Department of Mathematics,Computer Science and Statistics,Purdue University Calumet,Hammond,IN 46323-2094,USA School of Mathematical Sciences Fudan University Shanghai 200433 China Mathematical Institute University of Oxford 24-29 St Giles Oxford OX1 3LB UK Department of Mathematics Northwestern University Evanston IL 60208-2730 USA Department of Mathematics Computer Science and Statistics Purdue University Calumet Hammond IN 46323-2094 USA

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

关键词： conservation laws hyperbolic system fluid flow blood flow vessel hyper-bolicity Riemann problem Riemann solution wave curve shock wave rarefaction wave standing wave stability

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