Skip to main content
Springer Nature Link
Log in

Conservation laws with continuous flux functions

  • Published:
Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract

In the present paper we investigate uniqueness problem for generalized entropic solution of stationnary and evolution conservation laws under anisotropic conditions on vector-flux functions in the classesL ∞ andL ∞∩L 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [Ba, 1988] L. BARTHÉLEMY, Problème d'obstacle pour une équation quasilinéaire du premier ordre,Ann. Fac. Sci. Toulouse 9 2, 137–159 (1988)

    Google Scholar 

  • [Be, 1972] Ph. BÉNILAN,Equations d'évolution dans un espace de Banach quelconque et applications. Thèse Doctorat d'Etat, Université Paris Orsay, 1972

    Google Scholar 

  • [BK] Ph. BÉNILAN, S.N. KRUŽKOV, Uniqueness problem for first order equations with data fromL 1, (in preparation)

  • [Cr, 1972] M.G. CRANDALL, The semigroup approach to first order quasilinear equations in several spaces variables,Israel J. Math. 12, 108–122 (1972)

    Google Scholar 

  • [Kr, 1969 a] S.N. KRUŽKOV, Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications,Mat. Zam. 6 1, 97–98 (1969); English tr. inMath. Notes, V6, 517–523 (1969)

    Google Scholar 

  • [Kr, 1969 b] S.N. KRUŽKOV, Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order.,Dokl. Akad. Nauk SSSR 187, 1, 29–32 (1969); English tr. inSoviet Math. Dokl. 10 (1969)

    Google Scholar 

  • [Kr, 1970] S.N. KRUŽKOV, First order quasilinear equation in several independent variables. Mat. Sbornik81 2, 228–255 (1970); English tr. inMath. USSR Sb. 10 (1970)

    Google Scholar 

  • [KA, 1975] S.N. KRUŽKOV, P.A. ANDREJANOV, On the nonlocal theory of the Cauchy problem for quasi-linear equations of first order in the class of locally sommable functions,Dokl. Akad. Nauk SSSR 220 1, 23–26 (1975); English tr. inSoviet Math. Dokl. 16 (1975)

    Google Scholar 

  • [KH, 1974] S.N. KRUŽKOV, F. HILDEBRAND, The Cauchy problem for quasilinear first order equations in the case the domain of dependance on initial date is infinite,Vestnik Mosc. Univ. 1, 93–100 (1974); English tr. inMoscow Univ. Math. Bull. 29 (1974)

    Google Scholar 

  • [KP, 1990] S.N. KRUŽKOV, E.Yu. PANOV, Conservative quasilinear first-order laws with an infinite domain of dependance in the initial data,Dokl. Akad. Nauk. SSSR 314, 1 (1990); English tr. inSoviet Math. Dokl. 42 2, 316–321 (1991)

    Google Scholar 

  • [Pa, 1991] E.YU. PANOV.Generalized solutions of the Cauchy problem for quasilinear conservation laws. PhD dissertation, Fac. Mech. and Math. Moscow State Lomonossov University.

Download references

Author information

Authors and Affiliations

  1. Equipe de Mathématiques, U.R.A. CNRS 741, 25030, Besançon Cedex, France

    Philippe Bénilan

  2. Faculty of Mathematical and Mechanical Sciences, Moscow State Lomonossov University, 119899, Moscow, Russia

    Stanislzav Kružkov

Authors
  1. Philippe Bénilan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stanislzav Kružkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was performed while visiting the Equipe de Mathématiques in Besançon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bénilan, P., Kružkov, S. Conservation laws with continuous flux functions. NoDEA 3, 395–419 (1996). https://doi.org/10.1007/BF01193828

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01193828

Keywords

Search

Navigation