Skip to main content
Log in

Method of successive approximations for the Riemann problem with a small-amplitude discontinuity

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (Soc. Ind. Appl. Math., Philadelphia, 1972).

    Google Scholar 

  2. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).

    Google Scholar 

  3. V. Yu. Lyapidevskii and V. M. Teshukov, Mathematical Models of Long Wave Propagation in an Inhomogeneous Fluid (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].

    Google Scholar 

  4. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman and Hall/CRC, London, 2001).

    MATH  Google Scholar 

  5. V. V. Ostapenko, Hyperbolic Systems of Conservation Laws and Their Application to the Shallow Water Theory (Course of Lectures) (Novosibirsk, 2004) [in Russian].

  6. L. V. Ovsyannikov, Prikl. Mekh. Tekh. Fiz., No. 2, 3–13 (1979).

  7. P. E. Karabut and V. V. Ostapenko, Prikl. Mat. Mekh. 72, 958–970 (2009).

    MathSciNet  Google Scholar 

  8. V. V. Ostapenko, Prikl. Mat. Mekh. 65, 94–113 (2001).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. E. Karabut.

Additional information

Original Russian Text © P.E. Karabut, V.V. Ostapenko, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 1, pp. 9–15.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karabut, P.E., Ostapenko, V.V. Method of successive approximations for the Riemann problem with a small-amplitude discontinuity. Dokl. Math. 83, 143–148 (2011). https://doi.org/10.1134/S1064562411020025

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562411020025

Keywords

Navigation