An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 2, pp. 179-207.
partie suivante An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics 
@article{AIHPC_1988__5_2_179_0,
     author = {Le Floch, Ph. and Raviart, P. A.},
     title = {An asymptotic expansion for the solution of the generalized {Riemann} problem. {Part} {I} : general theory},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {179--207},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {2},
     year = {1988},
     mrnumber = {954470},
     zbl = {0679.35064},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1988__5_2_179_0/}
}
TY  - JOUR
AU  - Le Floch, Ph.
AU  - Raviart, P. A.
TI  - An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1988
SP  - 179
EP  - 207
VL  - 5
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1988__5_2_179_0/
LA  - en
ID  - AIHPC_1988__5_2_179_0
ER  - 
%0 Journal Article
%A Le Floch, Ph.
%A Raviart, P. A.
%T An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory
%J Annales de l'I.H.P. Analyse non linéaire
%D 1988
%P 179-207
%V 5
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1988__5_2_179_0/
%G en
%F AIHPC_1988__5_2_179_0
Le Floch, Ph.; Raviart, P. A. An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 2, pp. 179-207. http://www.numdam.org/item/AIHPC_1988__5_2_179_0/

[1] M. Ben-Artzi and J. Falcovitz, A Second Order Godunov-Type Scheme for Compressible Fluid Dynamics, J. Comp. Phys., Vol. 55, 1984, pp. 1-32. | MR | Zbl

[2] M. Ben-Artzi and J. Falcovitz, An Upwind Second-Order Scheme for Compressible Duct Flows, S.I.A.M. J. Sci. Stat. Comp., Vol. 7, 1986, pp. 744-768. | MR | Zbl

[3] A. Bourgeade, Ph. Le Floch and P.A. Raviart, Approximate Solution of the Generalized Riemann Problem and Applications, Actes du Congrès Hyperbolique of Saint-Etienne (France), January 1986, Springer-Verlag, 1988 (to appear). | MR | Zbl

[4] A. Bourgeade, Ph. Le Floch and P.A. Raviart, An Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Part. II: Application to the Gas Dynamics Equations (to appear). | Numdam

[5] J. Glimm, G. Marshall and B. Plohr, A Generalized Riemann Problem for Quasi-One-Dimensional Gas Flows, Adv. Appl. Maths., Vol. 5, 1984, pp. 1-30. | MR | Zbl

[6] E. Harabetian, A Cauchy-Kowalevky Theorem for Strictly Hyperbolic Systems of Conservation Laws with Piecewise Analytic Initial Data, Ph. D. dissertation, University of California, Los Angeles, 1984.

[7] Ph. Le Floch and P.A. Raviart, Un développement asymptotique pour la solution d'un problème de Riemann généralisé, C.R. Acad. Sci. Paris, T. 304, Séries I, n° 4, 1987. | MR | Zbl

[8] Li Tatsien and Yu Wenci, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke University Mathematics Series, 1985. | MR

[9] T.P. Liu, Quasilinear Hyperbolic Systems, Comm. Math. Phys., Vol. 68, 1979, pp. 141- 142. | MR | Zbl

[10] J. Smoller, Shock waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. | MR | Zbl

[11] B. Van Leer, Towards the Ultimate Conservative Difference Scheme, V, J. Comp. Phys., Vol. 32, 1979, pp. 101-136.