Skip to main content
SpringerLink
Log in

Boundary-value problems for hyperbolic equations with constant coefficients

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

By using a metric approach, we study the problem of well-posedness of boundary-value problems for hyperbolic equations of ordern (n≥2) with constant coefficients in a cylindrical domain. Conditions of existence and uniqueness of solutions are formulated in number-theoretic terms. We prove a metric theorem on lower estimates of small denominators that appear when constructing solutions.

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. B. I. Ptashnyk,Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  2. B. I. Ptashnyk and P. I. Shtabalyuk, “A boundary-value problem for hyperbolic equations in the class of functions almost periodic in space variables,”Differents. Uravn.,22, No. 4, 669–678 (1986).

    Google Scholar 

  3. I. O. Bobyk and B. I. Ptashnyk, “Boundary-value problems for hyperbolic equation with constant coefficients,” in:Abstracts of Ukrainian Conference on New Approaches to Solution of Differential Equations (Drogobych, January 25–27, 1994) [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994), p. 15.

    Google Scholar 

  4. I. O. Bobyk, Boundary-value problems for hyperbolic equations with constant coefficients,Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 6, 5–9 (1993).

    Google Scholar 

  5. J. Fritz, Restrictions on the coefficients of hyperbolic systems of partial differential equations,Proc. Natl. Acad. Sci. USA,74, No. 72, 4150–4151 (1977).

    Google Scholar 

  6. V. I. Bernyk, B. I. Ptashnyk, and B. O. Salyga, “An analog of the many-point problem for hyperbolic equations with constant coefficients”,Differents. Uravn.,13, No. 4, 637–645 (1977).

    Google Scholar 

  7. J. Sansone,Ordinary Differential Equations [Russian translation], Vol. 1, Inostrannaya Literatura, Moscow (1953).

    Google Scholar 

  8. V. G. Spryndzhuk,Metric Theory of Diophantine Approximations [in Russian], Nauka, Moscow (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lvov University, Lvov

    I. O. Bobyk

  2. Institute of Applied Mechanics and Mathematics, Ukrainian Academy of Sciences, Lvov

    B. I. Ptashnyk

Authors
  1. I. O. Bobyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. I. Ptashnyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 795–802, July, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobyk, I.O., Ptashnyk, B.I. Boundary-value problems for hyperbolic equations with constant coefficients. Ukr Math J 46, 869–877 (1994). https://doi.org/10.1007/BF01056663

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01056663

Keywords

Search

Navigation