The Heat Transfer Equation with an Unknown Heat Capacity Coefficient Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Output data | Year: 2020, Volume: 14, Number: 1, Pages: 104-114 Pages count : 11 DOI: 10.1134/S1990478920010111 | ||||
| Tags | existence; final-integral overdetermination conditions; heat capacity coefficient; heat transfer equation; inverse problem | ||||
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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. © 2020, Pleiades Publishing, Ltd.
Cite:
Kozhanov A.I.
The Heat Transfer Equation with an Unknown Heat Capacity Coefficient
Journal of Applied and Industrial Mathematics. 2020. V.14. N1. P.104-114. DOI: 10.1134/S1990478920010111 Scopus OpenAlex
The Heat Transfer Equation with an Unknown Heat Capacity Coefficient
Journal of Applied and Industrial Mathematics. 2020. V.14. N1. P.104-114. DOI: 10.1134/S1990478920010111 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85081998462 |
| OpenAlex: | W3012566480 |