Skip to main content
SpringerLink
Log in

Locally bounded solutions of one-dimensional conservation laws

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

A one-dimensional conservation law with a power-law flux function and an exponential initial condition is considered. We construct a generalized entropy solution with countably many shock waves. This solution is sign-alternating and one-sided periodic.

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

Access this article

Log in via an institution

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

  1. Evans, L.C., Partial Differential Equations, Providence, 1998.

    MATH  Google Scholar 

  2. Kruzhkov, S.N., Generalized Solutions of the Cauchy Problem in the Large for the First-Order Nonlinear Equations, Dokl. Akad. Nauk SSSR, 1969, vol. 187, no. 1, pp. 29–32.

    MathSciNet  MATH  Google Scholar 

  3. Kruzhkov, S.N., First-Order Quasilinear Equations with Several Independent Variables, Mat. Sb., 1970, vol. 81, no. 2, pp. 228–255.

    MathSciNet  MATH  Google Scholar 

  4. Goritskii, A.Yu. and Panov, E.Yu., On Locally Bounded Generalized Entropy Solutions of the Cauchy Problem for a First-Order Quasilinear Equation, Tr. Mat. Inst. Steklova, 2002, vol. 236, pp. 120–133.

    MathSciNet  Google Scholar 

  5. Goritsky, A.Yu. and Panov, E.Yu., Example of Nonuniqueness of Entropy Solutions in the Class of Locally Bounded Functions, Russ. J. Math. Phys., 1999, vol. 6, no. 4, pp. 492–494.

    MathSciNet  MATH  Google Scholar 

  6. Panov, E.Yu., On the Well-Posedness Classes of Locally Bounded Generalized Entropy Solutions of the Cauchy Problem for First-Order Quasilinear Equations, Fundam. Prikl. Mat., 2006, vol. 12, no. 5, pp. 175–178.

    Google Scholar 

  7. Goritskii, A.Yu., Kruzhkov, S.N., and Chechkin, G.A., Uravneniya s chastnymi proizvodnymi pervogo poryadka (First-Order Partial Differential Equations), Moscow, 1999.

    Google Scholar 

  8. Arnol’d, V.I., Geometricheskie metody v teorii obyknovennykh differentsial’nykh uravnenii (Geometric Methods in the Theory of Ordinary Differential Equations), Moscow, 2012.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    L. V. Gargyants

  2. Bauman Moscow State Technical University, Moscow, Russia

    L. V. Gargyants

Authors
  1. L. V. Gargyants
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. V. Gargyants.

Additional information

inal Russian Text © L.V. Gargyants, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 4, pp. 481–489.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gargyants, L.V. Locally bounded solutions of one-dimensional conservation laws. Diff Equat 52, 458–466 (2016). https://doi.org/10.1134/S0012266116040066

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266116040066

Keywords

Search

Navigation