Skip to main content
Log in

Solvability of boundary value problems for a class of Sobolev type equations in noncylindrical domains

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We prove the existence and uniqueness of a regular solution of a boundary value problem for a Sobolev type equation with elliptic-parabolic operators in noncylindrical domains.

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. Kozhanov, A.I., Solution Properties for a Class of Pseudoparabolic Equations, Dokl. Akad. Nauk, 1992, vol. 236, no. 5, pp. 781–786.

    MathSciNet  Google Scholar 

  2. Kozhanov, A.I., Certain Classes of Degenerate Sobolev-Galperin Equation, Siberian Adv. Math., 1994, vol. 4, no. 1, pp. 65–94.

    MATH  MathSciNet  Google Scholar 

  3. Kozhanov, A.I., Composite Type Equation and Inverse Problem, Utrecht, 1999.

    Book  Google Scholar 

  4. Pinigina, N.R., A Boundary Value Problem for Degenerate Ultraparabolic Equations of Sobolev Type, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 4, pp. 65–73.

    Google Scholar 

  5. Pinigina, N.R., Boundary Value Problem for a Class of Degenerate Systems of the Sobolev Type, Vestn. Novosibirsk. Gos. Univ. Mat. Mekh. Inform., 2012, vol. 12, no. 3, pp. 127–138.

    MATH  Google Scholar 

  6. Glazatov, S.N., Some Problems for Nonlinear Pseudo-Parabolic Equations in Noncylindrical Domains, Sibirsk. Mat. Zh., 2007, vol. 48, no. 2, pp. 272–289.

    MATH  MathSciNet  Google Scholar 

  7. Glazatov, S.N., On Two Problems of Electrodynamics Simulated by Nonlinear Pseudoparabolic Equations in Noncylindrical Domains, Preprint Inst. Math. Sib. Div. Russ. Acad. Sci., Novosibirsk, 2008, no. 216.

    Google Scholar 

  8. Kozhanov, A.I., A Remark on a Problem of Viscoelasticity and a Related Perturbed Wave Equation in Noncylindrical Domains, in Neklassicheskie uravneniya matematicheskoi fiziki (Nonclassical Equations of Mathematical Physics), Novosibirsk: Novosibirsk. Gos. Univ., 1993, pp. 99–103.

    Google Scholar 

  9. Kozhanov, A.I. and Lar’kin, N.A., On the Solvability of Boundary Value Problems for Strongly Nonlinear Equations of Viscoelasticity in Noncylindrical Domains, Mat. Zametki Yaroslavl. Gos. Univ., 1999, vol. 6, no. 1, pp. 36–45.

    MATH  Google Scholar 

  10. Yakubov, S.Ya., Lineinye differentsial’no-operatornye uravneniya i ikh prilozheniya (Linear Differential-Operator Equations and Their Applications), Baku, 1985.

    Google Scholar 

  11. Ladyzhenskaya, O.A. and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa (Linear and Quasilinear Equations of Elliptic Type), Moscow: Nauka, 1973.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. R. Pinigina.

Additional information

Original Russian Text © N.R. Pinigina, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 201–210.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pinigina, N.R. Solvability of boundary value problems for a class of Sobolev type equations in noncylindrical domains. Diff Equat 51, 204–213 (2015). https://doi.org/10.1134/S0012266115020068

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266115020068

Keywords

Navigation