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The Heat Transfer Equation with an Unknown Heat Capacity Coefficient

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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.

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Funding

The author was supported by the Russian Foundation for Basic Research (project no. 18-01-00620).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. I. Kozhanov

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    A. I. Kozhanov

Authors
  1. A. I. Kozhanov
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Correspondence to A. I. Kozhanov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2020, Vol. 23, No. 1, pp. 93–106.

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Kozhanov, A.I. The Heat Transfer Equation with an Unknown Heat Capacity Coefficient. J. Appl. Ind. Math. 14, 104–114 (2020). https://doi.org/10.1134/S1990478920010111

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  • DOI: https://doi.org/10.1134/S1990478920010111

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