Skip to main content
Log in

On global solvability of initial value problem for hyperbolic Monge–Ampère equations and systems

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

Abstract

The communication concerns a theory of global solvability of initial value problem for nonlinear hyperbolic equations with two independent variables that is an immediate analog of a theory of global solvability of ordinary differential equations.

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.

Similar content being viewed by others

References

  1. R. Courant, Methods of Mathematical Physics, Vol. 2: Partial Differential Equations (Interscience, New York, 1962; Moscow, Mir, 1964).

    Google Scholar 

  2. V. V. Lychagin, Russ. Math. 36 (5), 38–51 (1992).

    Google Scholar 

  3. B. L. Roždestvenskii and N. N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).

    Google Scholar 

  4. S. J. Bilčev, Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, 14–21 (1970).

    Google Scholar 

  5. A. M. Vasil’ev, Theory of Differential-Geometric Structures (Mosk. Gos. Univ., Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  6. P. D. Lax, J. Math. Phys. 5 (5), 611–613 (1964).

    Article  Google Scholar 

  7. N. J. Zabusky, J. Math. Phys. 3 (5), 1028–1039 (1962).

    Article  MathSciNet  Google Scholar 

  8. P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).

    MATH  Google Scholar 

  9. V. V. Kushner, V. V. Lychagin, and V. N. Rubtsov, Contact Geometry and Nonlinear Differential Equations (Cambridge Univ. Press, Cambridge, 2007).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. V. Tunitsky.

Additional information

Published in Russian in Doklady Akademii Nauk, 2017, Vol. 475, No. 5, pp. 500–502.

The article was translated by the author.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tunitsky, D.V. On global solvability of initial value problem for hyperbolic Monge–Ampère equations and systems. Dokl. Math. 96, 377–379 (2017). https://doi.org/10.1134/S1064562417040263

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417040263

Navigation