Skip to main content
SpringerLink
Log in

Uniqueness of the Solution of a Nonlocal Problem for an Elliptic-Hyperbolic Equation with Singular Coefficients

  • Research Articles
  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A boundary-value problem with nonlocal integral condition of Samarskii–Ionkin type is studied for a mixed-type equation with singular coefficients in a rectangular domain. A uniqueness criterion for the problem is established by the method of spectral analysis.

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. M. V. Keldysh, “On some cases of degeneracy of elliptic equations on the boundary of a domain,” Dokl. Akad. Nauk SSSR 77 (2), 181–183 (1951).

    Google Scholar 

  2. A. Weinstein, “Generalized axially symmetric potential theory,” Bull. Amer. Math. Soc. 59, 20–38 (1953).

    Article  MathSciNet  Google Scholar 

  3. I. A. Kipriyanov, Singular Elliptic Boundary-Value Problems (Nauka, Moscow, 1997) [in Russian].

    MATH  Google Scholar 

  4. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem,” Journal of Mathematical Sciences 216 (3), 345–496 (2016).

    Article  MathSciNet  Google Scholar 

  5. V. V. Katrakhov and S. M. Sitnik, “The transmutation method and boundary-value problems for singular elliptic equations,” in Singular Differential Equations, CMFD (Peoples’ Friendship University of Russia, Moscow, 2018), Vol. 64, pp. 211–426 [in Russian].

    MathSciNet  Google Scholar 

  6. E. L. Shishkina, “General Euler–Poisson–Darboux equation and hyperbolic \(B\)-potentials,” in Partial differential equations, CMFD (PFUR, Moscow, 2019), Vol. 65, pp. 157–338 [in Russian].

    MathSciNet  Google Scholar 

  7. L. I. Kamynin, “A boundary value problem in the theory of heat conduction with a nonclassical boundary condition,” U. S. S. R. Comput. Math. Math. Phys. 4 (6), 33–59 (1964).

    Article  Google Scholar 

  8. N. I. Ionkin, “Elliptic systems degenerating at a point,” Differ. Uravn. 13 (2), 276–284 (1977).

    MathSciNet  Google Scholar 

  9. A. A. Shkalikov, “Basis property of eigenfunctions of ordinary differential operators with integral boundary conditions,” Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., No. 6, 12–21 (1982).

    MathSciNet  Google Scholar 

  10. A. L. Skubachevskii, “Nonclassical boundary value problems. I,” Journal of Mathematical Sciences 155 (2), 199–334 (2008).

    Article  MathSciNet  Google Scholar 

  11. A. L. Skubachevskii, “Nonclassical boundary-value problems. II,” Journal of Mathematical Sciences 166 (4), 377–561 (2010).

    Article  MathSciNet  Google Scholar 

  12. I. S. Lomov, “Uniform convergence of root function expansions of a differential operator with integral boundary conditions,” Differ. Uravn. 55 (4), 486–497 (2019).

    Google Scholar 

  13. N. V. Zaitseva, “Boundary value problem with integral condition for the mixed type equation with a singular coefficient,” in Transmutation Operators and Applications, Trends in Math. (Birkhäuser, Cham, 2020), pp. 671–686.

    Article  MathSciNet  Google Scholar 

  14. V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  15. G. Watson, A Treatise on the Theory of Bessel Functions (Cambridge Univ. Press, Cambridge, 1945), Vol. 1.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. V. Zaitseva

Authors
  1. N. V. Zaitseva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. V. Zaitseva.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 544-551 https://doi.org/10.4213/mzm12909.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaitseva, N.V. Uniqueness of the Solution of a Nonlocal Problem for an Elliptic-Hyperbolic Equation with Singular Coefficients. Math Notes 109, 563–569 (2021). https://doi.org/10.1134/S000143462103024X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000143462103024X

Keywords

Search

Navigation