Geodesic
The heat transfer equation with an unknown heat capacity coefficient
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 93-106

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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.
Keywords: heat transfer equation, heat capacity coefficient, inverse problem, final-integral overdetermination conditions
Mots-clés : existence. 
@article{SJIM_2020_23_1_a8,
     author = {A. I. Kozhanov},
     title = {The heat transfer equation with an unknown heat capacity coefficient},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {93--106},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a8/}
}
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A. I. Kozhanov. The heat transfer equation with an unknown heat capacity coefficient. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 93-106. http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a8/