Skip to main content
SpringerLink
Log in

On a Variant of a Nonlocal Problem for a Quasilinear Equation with Rectilinear Characteristics

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

A nonlocal problem of Goursat type for a second-order quasilinear equation with rectilinear characteristics is investigated.

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. G.G. Bagaturia and M. Z. Menteshshvili, “On one variant of a nonlocal problem for a quasilinear hyperbolic equation,” Georgian Electron. Sci. J. Computer Sci. Telecommun., 3 (32) (2011).

  2. A. V. Bitsadze, Some Classes of Partial Differential Equations, Adv. Stud. Contemp. Math., 4, Gordon and Breach, New York (1988).

  3. R. Bitsadze, “On one version of the initial characteristic Darboux problem for one equation of nonlinear oscillation,” Rep. Enlarged Session Semin. JAM, 8, No. 1, 4–6 (1993).

    Google Scholar 

  4. E. Goursat, Leçons sur l’integration deséquations aux dérivées partielles du second ordre. Tome II: La méthode de Laplace. Les systèmes en involutions. La méthode de M. Darboux. Les équations de la première classe. Transformations des équations du second ordre. Généralisations diverses, Hermann, Paris (1898).

  5. J. Gvazava, “Some classes of hyperbolic equations and equations of mixed type,” Proc. A. Razmadze Math. Inst., 108 (1992).

  6. J. Gvazava, “Nonlocal and initial problems for quasilinear, nonstrictly hyperbolic equations with general solutions represented by superposition of arbitrary functions,” Georgian Math. J., 10, No. 4, 687–707 (2003).

    MathSciNet  MATH  Google Scholar 

  7. J. Gvazava, “The mean value property for nonstrictly hyperbolic second order quasilinear equations and the nonlocal problems,” Proc. A. Razmadze Math. Inst., 135, 79–96 (2004).

    MathSciNet  MATH  Google Scholar 

  8. J. Gvazava, “On a nonlocal characteristic problem for a class of quasilinear nonstrictly hyperboilic equations of second order,” Georgian Electron. Sci. J. Computer Sci. Telecommun., 4 (21), 89–93 (2009).

    Google Scholar 

  9. M. Z. Menteshashvili, “On the Cauchy problem with initial data on the unit circle,” Soobshch. Akad. Nauk Gruzii, 148, No. 2, 190–192 (1993).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Georgian Technical University, Tbilisi, Georgia

    R. Bitsadze

  2. N. I. Muskhelishvili Institute of Computational Mathematics of the Georgian Technical University, Tbilisi, Georgia

    M. Menteshashvili

  3. Sukhumi State University, Sukhumi, Georgia

    M. Menteshashvili

Authors
  1. R. Bitsadze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Menteshashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Bitsadze.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 90, Differential Equations and Mathematical Analysis, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bitsadze, R., Menteshashvili, M. On a Variant of a Nonlocal Problem for a Quasilinear Equation with Rectilinear Characteristics. J Math Sci 208, 655–660 (2015). https://doi.org/10.1007/s10958-015-2475-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2475-5

Keywords

Search

Navigation