Skip to main content
SpringerLink
Log in

Determining the boundary of a two-dimensional region from the solution of the external initial boundary-value problem for the heat equation

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

We determine the boundary of a two-dimensional region using the solution of the external initial boundary-value problem for the nonhomogeneous heat equation. The initial values for the boundary determination include the right-hand side of the equation and the solution of the initial boundary-value problem given for finitely many points outside the region. The inverse problem is reduced to solving a system of two integral equations nonlinear in the function defining the sought boundary. An iterative procedure is proposed for numerical solution of the problem involving linearization of integral equations. The efficiency of the proposed procedure is investigated by a computer experiment.

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. S. G. Golovina, A. M. Denisov, and V. I. Dmitriev, “An inverse problem of determining low-permeability zones in an oil-bearing layer,” Prikl. Mat. Informat., Moscow, No. 21, 5–14 (2005).

    Google Scholar 

  2. S. G. Golovina, “Linearization method in the inverse problem of determining low-permeability zones in an oil-bearing layer,” Vestnik MGU, Ser. 15: Vychil. Mat. Kibern., No. 1, 5–9 (2008).

  3. S. G. Golovina, and A. G. Razborov, “Determining the unknown boundary in a mixed problem for the heat equation,” Prikl. Matem. Informat., Moscow, No. 30, 18–24 (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    S. G. Golovina & A. G. Razborov

Authors
  1. S. G. Golovina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Razborov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Golovina.

Additional information

Translated from Prikladnaya Matematika i Informatika, No. 33, pp. 69–74, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golovina, S.G., Razborov, A.G. Determining the boundary of a two-dimensional region from the solution of the external initial boundary-value problem for the heat equation. Comput Math Model 21, 178–183 (2010). https://doi.org/10.1007/s10598-010-9061-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-010-9061-y

Keywords

Search

Navigation