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On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder

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Abstract

Under examination is the question on existence and uniqueness of solutions to some inverse problems for a parabolic equation. We look for a solution of this equation and a coefficient with the use of the data of an initial-boundary value problem and the Cauchy data on a part of the boundary of a spatial cylindrical domain. A solution is sought in Sobolev spaces and the coefficient in the class of continuous functions.

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Authors and Affiliations

  1. Khanty-Mansiĭsk Sobolev Institute of Mathematics, Yugra State University, Novosibirsk, Russia

    S. G. Pyatkov

  2. Yugra State University, Khanty-Mansiĭsk, Russia

    A. G. Borichevskaya

Authors
  1. S. G. Pyatkov
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  2. A. G. Borichevskaya
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Corresponding author

Correspondence to S. G. Pyatkov.

Additional information

Original Russian Text Copyright © 2013 Pyatkov S.G. and Borichevskaya A.G.

The authors were supported by the Russian Foundation for Basic Research (Grant 12-01-00260a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 436–449, March–April, 2013.

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Pyatkov, S.G., Borichevskaya, A.G. On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder. Sib Math J 54, 341–352 (2013). https://doi.org/10.1134/S003744661302016X

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  • DOI: https://doi.org/10.1134/S003744661302016X

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