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Sib. Zh. Ind. Mat., 2020, Volume 23, Number 1, Pages 93–106 (Mi sjim1080)  

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

Abstract: 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, existence.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00620_а


DOI: https://doi.org/10.33048/SIBJIM.2020.23.109

Full text: PDF file (589 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 517.946
Received: 01.07.2019
Revised: 01.07.2019
Accepted:05.12.2019

Citation: A. I. Kozhanov, “The heat transfer equation with an unknown heat capacity coefficient”, Sib. Zh. Ind. Mat., 23:1 (2020), 93–106

Citation in format AMSBIB
\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}


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