Abstract:
Under study are the inverse problems of finding,
together with a solution u(x,t)
of the differential equation
cut−Δu+a(x,t)u=f(x,t)
describing the process of heat distribution,
some real c characterizing the heat capacity of the medium
(under the assumption that the medium is homogeneous).
Not only the initial condition is imposed on u(x,t),
but also the usual conditions of the first or second initial-boundary value problems
as well as some special overdetermination conditions.
We prove the theorems of existence of a solution (u(x,t),c)
such that u(x,t) has all Sobolev generalized derivatives
entered into the equation, while c is a positive number.
Citation:
A. I. Kozhanov, “The heat transfer equation with an unknown heat capacity coefficient”, Sib. Zh. Ind. Mat., 23:1 (2020), 93–106; J. Appl. Industr. Math., 14:1 (2020), 104–114
\Bibitem{Koz20}
\by A.~I.~Kozhanov
\paper The heat transfer equation with an unknown heat capacity coefficient
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 1
\pages 93--106
\mathnet{http://mi.mathnet.ru/sjim1080}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.109}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 1
\pages 104--114
\crossref{https://doi.org/10.1134/S1990478920010111}
Linking options:
https://www.mathnet.ru/eng/sjim1080
https://www.mathnet.ru/eng/sjim/v23/i1/p93
This publication is cited in the following 3 articles:
S. G. Pyatkov, O. A. Soldatov, “On some classes of inverse parabolic problems of recovering the thermophysical parameters”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:3 (2023), 23–33
V. I. Vasil'ev, A. M. Kardashevsky, “Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation”, J. Appl. Industr. Math., 15:2 (2021), 343–354
Citation in format AMSBIB
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