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Computational Mathematics and Modeling

, Volume 22, Issue 3, pp 238–245 | Cite as

Determining the internal boundary of a region in the two-dimensional initial–boundary-value problem for the heat equation

  • S. G. Golovina
  • A. G. Razborov
Article

The article investigates the reconstruction of the internal boundary of a two-dimensional region in the two-dimensional initial–boundary-value problem for the homogeneous heat equation. The initial values for the determination of the internal boundary are provided by a boundary condition of second kind on the external boundary and the solution of the initial–boundary-value problem at finitely many points inside the region. The inverse problem is reduced to solving a system of integral equations nonlinear in the function describing the sought boundary. An iterative numerical procedure is proposed involving linearization of integral equations.

Keywords

inverse problems numerical methods boundary reconstruction 

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References

  1. 1.
    S. G. Golovina, A. M. Denisov, and V. I. Dmitriev, “Inverse problem of determining low-permeability zones in an oil-bearing layer,” Prikl. Matem. Informatika, No. 21, 5–14, MAKS Press, Moscow (2005).Google Scholar
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    S. G. Golovina, “Linearization method in the inverse problem of determining low-permeability zones in an oil-bearing layer,” Vestnik MGU, Ser. 15: Vychisl. Matem. Kibern., No. 1, 5–9 (2008).Google Scholar
  3. 3.
    S. G. Golovina and A. G. Razborov, “Determining the boundary of a two-dimensional region from the solution of an external initial–boundary-value problem for the heat equation,” Prikl. Matem. Informatika, No. 33, 69–74, MAKS Press, Moscow (2009).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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