摘要
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.
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.
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
基金
supported in part by the National Science Foundation under Grants DMS-0935967
the National Science Foundation under Grants DMS-0807551
the National Science Foundation under Grants DMS-0720925
the National Science Foundation under Grants DMS-0505473
the Natural Science Foundation of China under Grant NSFC-10728101,and the Royal Society-Wolfson Research Merit Award (UK)
