Skip to main content
SpringerLink
Log in

On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A mixed problem with nonlocal conditions on a space variable is considered for a system of quasilinear first-order hyperbolic equations with two independent variables. The sufficient conditions of solvability of this system are given.

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

References

  1. B. I. Ptashnik,Incorrect Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  2. V. M. Kirilich, “A nonclassical problem with integral restrictions for a two-dimensional first-order hyperbolic system,”Vestn. L'vov. Univ. Ser. Mech. Mat., Issue 21, 60–64, L'vov (1983).

  3. V. M. Kirilich, “A nonclassical boundary-value problem for a two-dimensional first-order hyperbolic system with discontinuous coefficients,” in:The General Theory of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1983), p. 267.

    Google Scholar 

  4. Z. O. Mel'nik, “A nonclassical boundary-value problem for a hyperbolic system with two independent variables,”Differents. Uravn.,17, No. 6, 1096–1104 (1981).

    Google Scholar 

  5. Z. O. Mel'nik, “A problem with integral restrictions for a second-order hyperbolic equation,” in:The General Theory of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1983), pp. 281–282.

    Google Scholar 

  6. Z. O. Mel'nik, “A problem with integral restrictions for general two-dimensional hyperbolic equations and systems,”Differents. Uravn.,21, No. 2, 246–253 (1985).

    Google Scholar 

  7. Z. O. Mel'nik and V. M. Kirilich, “A problem with integral restrictions for hyperbolic equations on a straight line without initial conditions,”Ukr. Mat. Zh.,35, No. 6, 722–727 (1983).

    Google Scholar 

  8. I. Ya. Kmit',On Nonlocal Problems for First-Order Hyperbolic Systems [in Russian], Dep. UkrNIINTI No.79-Uk.91, L'vov (1991).

  9. V.É. Abolinya and A. D. Myshkis, “A mixed problem for an almost linear hyperbolic system on a plane,”Mat. Sb.,50, No. 2, 423–442 (1960).

    Google Scholar 

  10. A. D. Myshkis and A. M. Filimonov, “Continuous solutions of quasilinear hyperbolic systems with two independent variables,”Differents. Uravn.,17, No. 3, 488–500 (1981).

    Google Scholar 

  11. A. M. Filimonov,Sufficient Conditions of the Global Solvability of a Mixed Problem for Quasilinear Hyperbolic Systems with Two Independent Variables [in Russian], Dep. VINITI No.6-81, Moscow (1980).

  12. N. P. Erugin, I. Z. Shtokalo, P. S. Bondarenko, et al.,A Course of Ordinary Differential Equations [in Russian], Vyshcha Shkola, Kiev (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. L'vov University, L'vov

    I. Ya. Kmit'

Authors
  1. I. Ya. Kmit'
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1307–1311, September, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kmit', I.Y. On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables. Ukr Math J 45, 1465–1470 (1993). https://doi.org/10.1007/BF01058645

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058645

Keywords

Search

Navigation