The heat transfer equation with an unknown heat capacity coefficient
A. I. Kozhanovab
a Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
b Sobolev Institute of Mathematics, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
Under study are the inverse problems of finding,
together with a solution $u(x,t)$
of the differential equation
$cu_t -\Delta u + a(x,t)u = f(x,t)$
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.
heat transfer equation, heat capacity coefficient, inverse problem,
final-integral overdetermination conditions, existence.
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A. I. Kozhanov, “The heat transfer equation with an unknown heat capacity coefficient”, Sib. Zh. Ind. Mat., 23:1 (2020), 93–106
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\paper The heat transfer equation with an unknown heat capacity coefficient
\jour Sib. Zh. Ind. Mat.
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