Skip to main content
SpringerLink
Log in

Approximation of the Bitsadze-Samarskii inverse problem for an elliptic equation with the dirichlet conditions

  • Numerical Methods
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

An inverse problem for an elliptic equation in a Banach space with the Bitsadze-Samarskii conditions is considered. The suggested approach uses the notion of a general approximation scheme, the theory of C 0-semigroups of operators, and methods of functional 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. Krein, S.G. and Laptev, G.I., Boundary Value Problems for Second Order Differential Equations in a Banach Space. I, Differ. Uravn., 1966, vol. 2, no. 3, pp. 382–390.

    MathSciNet  MATH  Google Scholar 

  2. Krein, S.G. and Laptev, G.I., Well-Posedness of Boundary Value Problems for a Differential Equation of the Second Order in a Banach Space. II, Differ. Uravn., 1966, vol. 2, no. 7, pp. 919–926.

    MathSciNet  Google Scholar 

  3. Orlovsky, D. and Piskarev, S., On Approximation of Inverse Problems for Abstract Elliptic Problems, J. Inverse Ill-Posed Probl., 2009, vol. 17, no. 8, pp. 765–782.

    Article  MathSciNet  MATH  Google Scholar 

  4. Prilepko, A.I., Orlovsky, D.G., and Vasin, I.A., Methods for Solving Inverse Problems in Mathematical Physics, New York; Basel, 2000.

    MATH  Google Scholar 

  5. Orlovskii, D.G., An Inverse Problem for a Second-Order Differential Equation in a Banach Space, Differ. Uravn., 1989, vol. 25, no. 6, pp. 1000–1009.

    MathSciNet  Google Scholar 

  6. Orlovskii, D.G., On a Problem of Determining the Parameter of an Evolution Equation, Differ. Uravn., 1990, vol. 26, no. 9, pp. 1614–1621.

    MathSciNet  Google Scholar 

  7. Prilepko, A.I., Selected Questions in Inverse Problems of Mathematical Physics, in Uslovno-korrektnye zadachi matematicheskoi fiziki i analiza (Conditionally Well-Posed Problems in Mathematical Physics and Analysis), Novosibirsk, 1992, pp. 151–162.

    Google Scholar 

  8. Prilepko, A.I., Inverse Problems of Potential Theory (Elliptic, Parabolic, Hyperbolic Equation and Transport Equations), Mat. Zametki, 1973, vol. 14, no. 6, pp. 755–767.

    MathSciNet  Google Scholar 

  9. Solov’ev, V.V., Inverse Problems of Source Determination for the Poisson Equation on the Plane, Zh. Vychisl. Mat. Mat. Fiz., 2004, vol. 44, no. 5, pp. 862–871.

    MathSciNet  MATH  Google Scholar 

  10. Krein, S.G. and Laptev, G.I., Boundary Value Problems for an Equation in Hilbert Space, Dokl. Akad. Nauk SSSR, 1962, vol. 146, no. 3, pp. 535–538.

    MathSciNet  Google Scholar 

  11. Clement, Ph., Heijmans, H.J.A.M., Angenent, S., et al., One-Parameter Semigroups, CWI Monographs, 5, Amsterdam, 1987.

    MATH  Google Scholar 

  12. Sidorov, Yu.V., Fedoryuk, M.V., and Shabunin, M.I., Lektsii po teorii funktsii kompleksnogo peremennogo (Lectures in the Theory of Functions of a Complex Variable), Moscow: Nauka, 1982.

    Google Scholar 

  13. Grigorieff, R.D., Diskrete Approximation von Eigenwertproblemen. II, Konvergenzordnung. Numer. Math., 1975, vol. 24, no. 5, pp. 415–433.

    Article  MathSciNet  MATH  Google Scholar 

  14. Stummel, F., iskrete Konvergenz linearer Operatoren. III, Linear Operators and Approximation: Proc. Conf. Oberwolfach, 1971. Internat. Ser. Numer. Math., vol. 20, Basel, 1972, pp. 196–216.

    Google Scholar 

  15. Vainikko, G., Funktionalanalysis der Diskretisierungsmethoden, Leipzig, 1976.

    MATH  Google Scholar 

  16. Vainikko, G., Approximative Methods for Nonlinear Equations (Two Approaches to the Convergence Problem), Nonlinear Anal., 1978, vol. 2, pp. 647–687.

    Article  MathSciNet  MATH  Google Scholar 

  17. Piskarev, S., On Approximation of Holomorphic Semigroups, Tartu Riikl. Ul. Toimetised, 1979, no. 492, pp. 3–23.

    Google Scholar 

  18. Piskarev, S.I., Differentsial’nye uravneniya v banakhovom prostranstve i ikh approksimatsiya (Differential Equations in a Banach Space and Their Approximation), Moscow, 2005.

    Google Scholar 

  19. Ashyralyev, A. and Ozturk, E., On Bitsadze-Samarskii Type Nonlocal Boundary Value Problems for Elliptic Differential and Difference Equations: Well-Posedness, Appl. Math. Comput., 2013, vol. 219, no. 3, pp. 1093–1107.

    Article  MathSciNet  Google Scholar 

  20. Li Miao, Morozov, V., and Piskarev, S., On the Approximations of Derivatives of Integrated Semigroups. II, J. Inverse Ill-Posed Probl., 2011, vol. 19,iss. 3–4, pp. 643–688.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Engineering and Physics (State University), Moscow, Russia

    D. G. Orlovskii & S. I. Piskarev

  2. Moscow State University, Moscow, Russia

    D. G. Orlovskii & S. I. Piskarev

Authors
  1. D. G. Orlovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. I. Piskarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © D.G. Orlovskii, S.I. Piskarev, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 7, pp. 923–935.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Orlovskii, D.G., Piskarev, S.I. Approximation of the Bitsadze-Samarskii inverse problem for an elliptic equation with the dirichlet conditions. Diff Equat 49, 895–907 (2013). https://doi.org/10.1134/S0012266113070112

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266113070112

Keywords

Search

Navigation