The Riemann problem for a class of resonant hyperbolic systems of balance laws
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 6, pp. 881-902. 
@article{AIHPC_2004__21_6_881_0,
     author = {Goatin, Paola and Le Floch, Philippe G.},
     title = {The {Riemann} problem for a class of resonant hyperbolic systems of balance laws},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {881--902},
     publisher = {Elsevier},
     volume = {21},
     number = {6},
     year = {2004},
     doi = {10.1016/j.anihpc.2004.02.002},
     mrnumber = {2097035},
     zbl = {1086.35069},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.02.002/}
}
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Goatin, Paola; Le Floch, Philippe G. The Riemann problem for a class of resonant hyperbolic systems of balance laws. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 6, pp. 881-902. doi : 10.1016/j.anihpc.2004.02.002. http://www.numdam.org/articles/10.1016/j.anihpc.2004.02.002/

[1] Amadori D., Gosse L., Guerra G., Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws, Arch. Rational Mech. Anal. 162 (2002) 327-366. | MR | Zbl

[2] Amadori D., Gosse L., Guerra G., Godunov-type approximation for a general resonant balance law with large data, J. Differential Equations 198 (2004) 233-274. | MR | Zbl

[3] N. Andrianov, G. Warnecke, The Riemann problem for the Baer-Nunziato model of two-phase flows, J. Comput. Phys., in press. | Zbl

[4] N. Andrianov, G. Warnecke, On the solution to the Riemann problem for the compressible duct flow, SIAM J. Appl. Math., in press. | MR | Zbl

[5] Andrianov N., Saurel R., Warnecke G., A simple method for compressible multiphase mixtures and interfaces, Int. J. Num. Meth. Fluids 41 (2003) 109-131. | MR | Zbl

[6] F. Asakura, Global solutions with a single transonic shock wave for quasilinear hyperbolic systems, submitted for publication. | MR | Zbl

[7] Botchorishvili R., Perthame B., Vasseur A., Equilibrium schemes for scalar conservation laws with stiff sources, Math. of Comput. 72 (2003) 131-157. | MR | Zbl

[8] F. Bouchut, An introduction to finite volume methods for hyperbolic systems of conservation laws with source, INRIA Rocquencourt Report, 2002.

[9] Chen G.-Q., Glimm J., Global solutions to the compressible Euler equations with geometrical structure, Comm. Math. Phys. 180 (1996) 153-193. | MR | Zbl

[10] Clarke F.H., Optimization and Non-Smooth Analysis, Classics in Applied Mathematics, vol. 5, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. | MR | Zbl

[11] Courant R., Friedrichs K.O., Supersonic Flow and Shock Waves, Wiley, New York, 1948. | MR | Zbl

[12] Dal Maso G., Lefloch P.G., Murat F., Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995) 483-548. | MR | Zbl

[13] Embid P., Goodman J., Majda J., Multiple steady states for 1-D transonic flows, SIAM J. Sci. Stat. Comput. 5 (1984) 21-41. | MR | Zbl

[14] Glimm J., Marschall G., Plohr B., A generalized Riemann problem for quasi-one-dimensional gas flows, Adv. Appl. Math. 5 (1981) 1-30. | MR | Zbl

[15] Gosse L., A well-balanced scheme using non-conservative products designed for hyperbolic conservation laws with source-terms, Math. Model Methods Appl. Sci. 11 (2001) 339-365. | MR | Zbl

[16] Greenberg J.M., Leroux A.Y., A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J. Numer. Anal. 33 (1996) 1-16. | MR | Zbl

[17] Hartman P., Ordinary Differential Equations, Wiley, New York, 1964. | MR | Zbl

[18] Isaacson E., Temple B., Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Math. 52 (1992) 1260-1278. | MR | Zbl

[19] Isaacson E., Temple B., Convergence of the 2×2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55 (1995) 625-640. | MR | Zbl

[20] Jin S., Wen X., An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, J. Comp. Math. 2 (2004) 230-249. | MR | Zbl

[21] S. Jin, X. Wen, Two interface numerical methods for computing hyperbolic systems with geometrical source terms having concentrations, SIAM J. Sci. Com., in press. | Zbl

[22] Lefloch P.G., Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, Comm. Partial Differential Equations 13 (1988) 669-727. | MR | Zbl

[23] P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math. and its Appl., Minneapolis, Preprint # 593, 1989.

[24] Lefloch P.G., An existence and uniqueness result for two nonstrictly hyperbolic systems, in: Keyfitz B.L., Shearer M. (Eds.), Nonlinear Evolution Equations that Change Type, IMA Volumes in Math. and its Appl., vol. 27, Springer-Verlag, 1990, pp. 126-138. | MR | Zbl

[25] Lefloch P.G., Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002. | MR | Zbl

[26] Lefloch P.G., Thanh M.D., The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Comm. Math. Sci. 1 (2003) 763-797. | MR | Zbl

[27] Lien W.C., Hyperbolic conservation laws with a moving source, Comm. Pure Appl. Math. 52 (1999) 1075-1098. | MR | Zbl

[28] Liu T.-P., Quasilinear hyperbolic systems, Comm. Math. Phys. 68 (1979) 141-172. | MR | Zbl

[29] Liu T.-P., Nonlinear stability and instability of transonic flows through a nozzle, Comm. Math. Phys. 83 (1982) 243-260. | MR | Zbl

[30] Liu T.-P., Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28 (1987) 2593-2602. | MR | Zbl

[31] D. Marchesin, P.J. Paes-Leme, A Riemann problem in gas dynamics with bifurcation, PUC Report MAT 02/84, 1984.

[32] Marchesin D., Plohr B., Schecter S., An organizing center for wave bifurcation flow models, SIAM J. Appl. Math. 57 (1997) 1189-1215. | MR | Zbl

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