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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 2, Pages 436–449 (Mi smj2431)  
On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder

S. G. Pyatkovab, A. G. Borichevskayaa

a Yugra State University, Khanty-Mansiĭsk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
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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.
Keywords: inverse problem, second order parabolic equation, boundary value problem, overdetermination condition.
Received: 04.04.2012
Revised: 27.09.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 2, Pages 341–352
DOI: https://doi.org/10.1134/S003744661302016X
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: S. G. Pyatkov, A. G. Borichevskaya, “On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder”, Sibirsk. Mat. Zh., 54:2 (2013), 436–449; Siberian Math. J., 54:2 (2013), 341–352
Citation in format AMSBIB
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\vol 54
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\pages 436--449
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