Skip to main content
SpringerLink
Log in

On the Restoration of Initial Data of a Boundary-Value Problem for a Second-Order Parabolic Equation

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

On the basis of the Fourier expansion of a generalized function in a complete orthonormal system of fundamental functions of an elliptic operator, we propose an approximate method for determination of the initial data of a boundary-value problem for a second-order parabolic equation.

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. A. Aleksidze, Fundamental Functions in Approximate Solutions of Boundary-Value Problems [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  2. A. B. Bakushinskii, "Remarks on the Kupradze-Aleksidze method," Differents. Uravn., 6, No. 7, 1298-1301 (1970).

    Google Scholar 

  3. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  4. B. V. Hera, "Restoration of the fields of temperature and humidity in a porous body in the case of incomplete data," Mat. Met. Fiz.-Mekh. Polya, 39, No. 1, 66-73 (1996).

    Google Scholar 

  5. S. D. Ivasishen, Green Matrices of Parabolic Boundary-Value Problems [in Russian], Vyshcha Shkola, Kiev (1990).

    Google Scholar 

  6. H. P. Lopushans'ka, "On an approximate method for solution of a generalized Dirichlet problem," Ukr. Mat. Zh., 46, No. 10, 1417-1420 (1994).

    Google Scholar 

  7. H. P. Lopushans'ka, "On an approach to the study of boundary-value problems in spaces of distributions and boundary integral equations," Ukr. Mat. Zh., 43, No. 5, 632-639 (1991).

    Google Scholar 

  8. I. Ya. Mekh, "On the fundamental solutions of elliptic operators," Dokl. Akad. Nauk Ukr. SSR, No. 5, 14-18 (1991). 1196

  9. I. Ya. Roitberg and Ya. A. Roitberg, "On the approximation of solutions of elliptic boundary-value problems by linear combinations of fundamental solutions," Dokl. Akad. Nauk Ukrainy, No. 12, 15-20 (1992).

  10. Ya. A. Roitberg, Elliptic Boundary Value Problems in the Spaces of Distributions, Kluwer, Dordrecht (1996).

    Google Scholar 

  11. Ya. A. Roitberg, "Elliptic problems with inhomogeneous boundary conditions and a local increase in smoothness up to the bound of generalized solutions," Dokl. Akad. Nauk SSSR, 157, No. 4, 798-801 (1964).

    Google Scholar 

  12. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).

    Google Scholar 

  13. S. D. Eidel'man, Parabolic Systems [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  14. J.-L. Lions, "Remarks on systems with uncomplete data," in: Proceedings of the International Symposium "Variational Methods in Geosciences" (October 1985, Norman, Oklahoma), Elsevier, Amsterdam (1986), pp. 145-159.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Franko State University, Lviv

    H. P. Lopushans'ka

Authors
  1. H. P. Lopushans'ka
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lopushans'ka, H.P. On the Restoration of Initial Data of a Boundary-Value Problem for a Second-Order Parabolic Equation. Journal of Mathematical Sciences 109, 1188–1196 (2002). https://doi.org/10.1023/A:1013784308916

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013784308916

Keywords

Search

Navigation