- D. Amadori, L. Gosse and G. Guerra, Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws. Arch. Ration. Mech. Anal. 162 (2002) 327–366. [CrossRef] [MathSciNet]
- A. Bressan, Hyperbolic Systems of Conservation Laws: the One-dimensional Cauchy Problem. Oxford University Press (2000).
- R.J. DiPerna, Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ. Math. J. 28 (1979) 202–212.
- T.N. Dinh, R.R. Nourgaliev and T.G. Theofanous, Understanding the ill-posed two-fluid model , in Proc. of the 10th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10) Seoul, Korea (October 2003).
- D.A. Drew and S.L. Passman, Theory of Multicomponent Fluids . Springer, New York (1999).
- S.K. Godunov, An interesting class of quasilinear systems. Dokl. Akad. Nauk SSR 139 (1961) 521–523.
- M. Ishii, Thermo-fluid dynamic theory of two-phase flow . Eyrolles, Paris (1975).
- B.L. Keyfitz, R. Sanders and M. Sever, Lack of hyperbolicity in the two-fluid model for two-phase incompressible flow . Discrete Contin. Dynam. Systems, Series B 3 (2003) 541–563.
- B.L. Keyfitz, M. Sever and F. Zhang, Viscous singular shock structure for a nonhyperbolic two-fluid model. Nonlinearity 17 (2004) 1731–1747. [CrossRef] [MathSciNet]
- H.-O. Kreiss and J. Ystrom, Parabolic problems which are ill-posed in the zero dissipation limit . Math. Comput. Model. 35 (2002) 1271–1295. [CrossRef]
- M.S. Mock, Systems of conservation laws of mixed type . J. Diff. Equations 37 (1980) 70–88. [CrossRef]
- H. Ransom and D.L. Hicks, Hyperbolic two-pressure models for two-phase flow . J. Comput. Phys. 53 (1984) 124–151. [CrossRef] [MathSciNet]
- R. Sanders and M. Sever, Computations with singular shocks (2005) (preprint).
- S. Sever, A model of discontinuous, incompressible two-phase flow (2005) (preprint).
- H.B. Stewart and B. Wendroff, Two-phase flow: models and methods . J. Comput. Phys. 56 (1984) 363–409. [CrossRef] [MathSciNet]
Volume 39, Number 1, January-February 2005
|Page(s)||37 - 58|
|Published online||15 March 2005|