An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory

Ph. Le Floch; P. A. Raviart

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 2, page 179-207
  • ISSN: 0294-1449

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Le Floch, Ph., and 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 5.2 (1988): 179-207. <http://eudml.org/doc/78149>.

@article{LeFloch1988,
author = {Le Floch, Ph., Raviart, P. A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear hyperbolic system of conservation laws in two dimensions; existence and uniqueness of solution; Riemann problem; asymptotic expansion},
language = {eng},
number = {2},
pages = {179-207},
publisher = {Gauthier-Villars},
title = {An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory},
url = {http://eudml.org/doc/78149},
volume = {5},
year = {1988},
}

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
PB - Gauthier-Villars
VL - 5
IS - 2
SP - 179
EP - 207
LA - eng
KW - nonlinear hyperbolic system of conservation laws in two dimensions; existence and uniqueness of solution; Riemann problem; asymptotic expansion
UR - http://eudml.org/doc/78149
ER -

References

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  1. [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. Zbl0535.76070MR757422
  2. [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. Zbl0594.76057MR848562
  3. [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). Zbl0644.65059MR910100
  4. [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). 
  5. [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. Zbl0566.76056MR736548
  6. [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. [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. Zbl0619.35074MR890629
  8. [8] Li Tatsien and Yu Wenci, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke University Mathematics Series, 1985. MR823237
  9. [9] T.P. Liu, Quasilinear Hyperbolic Systems, Comm. Math. Phys., Vol. 68, 1979, pp. 141- 142. Zbl0435.35054MR543196
  10. [10] J. Smoller, Shock waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. Zbl0508.35002MR688146
  11. [11] B. Van Leer, Towards the Ultimate Conservative Difference Scheme, V, J. Comp. Phys., Vol. 32, 1979, pp. 101-136. 

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