The Riemann problem for p -systems with continuous flux function

Boris P. Andreianov

Annales de la Faculté des sciences de Toulouse : Mathématiques (1999)

  • Volume: 8, Issue: 3, page 353-367
  • ISSN: 0240-2963

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Andreianov, Boris P.. "The Riemann problem for $p$-systems with continuous flux function." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.3 (1999): 353-367. <http://eudml.org/doc/73492>.

@article{Andreianov1999,
author = {Andreianov, Boris P.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {selfsimilar solution; vanishing viscosity; non-Lipschitz flux function},
language = {eng},
number = {3},
pages = {353-367},
publisher = {UNIVERSITE PAUL SABATIER},
title = {The Riemann problem for $p$-systems with continuous flux function},
url = {http://eudml.org/doc/73492},
volume = {8},
year = {1999},
}

TY - JOUR
AU - Andreianov, Boris P.
TI - The Riemann problem for $p$-systems with continuous flux function
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1999
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 3
SP - 353
EP - 367
LA - eng
KW - selfsimilar solution; vanishing viscosity; non-Lipschitz flux function
UR - http://eudml.org/doc/73492
ER -

References

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  1. [1] Andreyanov ( B.). — "Solutions auto-similaires du problème de Riemann pour une loi de conservation scalaire quasilinéaire à fonction de flux continue avec la viscosité ∈tuxx" Publ. Math. Besançon, An. non-linéaire, V.15 (1995/97), pp.127-131. Zbl1006.35063MR1773619
  2. [2] Andreyanov ( B.). — "Vanishing viscosity method and explicit formulae for solutions of the Riemann problem for scalar conservation laws" Vestn. Mosc. Univ.I (1999), No.1, pp.3-8. Zbl0951.35077MR1704323
  3. [3] Andreianov ( B.). — Ph. D. thesis, Univ. Franche-Comté, 2000. 
  4. [4] Chang ( T.), Hsiao ( L.) ( T. Zhang, L. Xiao). — "The Riemann Problem and Interaction of Waves in Gas Dynamics" PitmanMonographs and Surveys in Pure and Appl. Math., 41 (1989). Zbl0698.76078MR994414
  5. [5] Dafermos ( C.M.). — "Structure of solutions of the Riemann problem for hyperbolic systems of conservation laws" Arch. Rat. Mech. Anal., V.53 (1974), No.3, pp.203-217. Zbl0278.35065MR348289
  6. [6] Gelfand ( I.M.). — "Some problems in the theory of quasilinear equations" Uspekhi Mat. Nauk, V.14 (1959), No. 2, pp. 87-158; English tr. in Amer. Math. Soc. Transl. Ser. V.29 (1963), No.2, pp.295-381. Zbl0127.04901MR110868
  7. [7] Krejčí ( P.), Straškraba ( I.). — "A uniqueness criterion for the Riemann problem" Mat.Ústav AV ČR, V.84 (1993); Hiroshima Math. J. V. 27 (1997), No. 2, pp. 307-346. Zbl0883.35079MR1461177
  8. [8] Kruzhkov ( S.N.). — "Nonlinear partial differential equations" Part II. (Lections 3,4) Mosc. St. Univ. edition, 1970. 
  9. [9] Leibovich ( L.). - "Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions" J. Math. Anal. Appl., V.45 (1974), No. 3, pp. 81-90. Zbl0273.35052MR348278
  10. [10] Tzavaras ( A.E.).— "Elastic as limit of viscoelastic response, in a context of selfsimilar viscous limits" J. Diff. Eq., V.123 (1995), No. 1, pp. 305-341. Zbl0853.73015MR1359921
  11. [11] Tzavaras ( A.E.). — "Viscosity and relaxation approximations for hyperbolic systems of conservation laws" in "An introduction to recent developments in theory and numerics of conservation laws", D. Kroener & al., eds.; Lect. Notes in Comp. Sci. and Engin., V.5, Springer, 1998, pp. 73-122. Zbl0969.74006
  12. [12] Wendroff ( B.). — "The Riemann problem for materials with nonconcave equations of state. I: Isentropic flow" J. Math. Anal. Appl., V. 38 (1972), pp. 454-466. Zbl0264.76054MR328387

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