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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 3, Pages 83–97
DOI: https://doi.org/10.26907/0021-3446-2021-3-83-97 (Mi ivm9660) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Inverse problems for a two-dimensional heat equation with unknown right-hand side

K. B. Sabitovab, A. R. Zainullovb

a Institute for Strategic Studies of the Republic of Bashkortostan, 68 Odessa str., Sterlitamak, 453103 Russia
b Sterlitamak branch of Bashkir State University, 49 Lenin Ave., Sterlitamak, 453103 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-3-83-97
Abstract: Based on the solution of the first initial-boundary value problem for the inhomo-geneous two-dimensional heat equation, the inverse problems are posed and studied to find the factors of the right-hand side depending on spatial variables and time. Previously, the solution of the direct initial-boundary-value problem is constructed explicitly. The uniqueness of the solution of the direct and inverse problems is proved on the basis of the completeness property of the system of eigenfunctions of the corresponding homogeneous Dirichlet problem for the Laplace operator. Existence theorems for solving inverse problems are established. The solutions of which are built explicitly.
Keywords: heat equation, initial-boundary value problem, inverse problem, uniqueness, series, existence, integral equation.
Received: 29.04.2020
Revised: 30.06.2020
Accepted: 01.10.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 3, Pages 75–88
DOI: https://doi.org/10.3103/S1066369X21030087
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, A. R. Zainullov, “Inverse problems for a two-dimensional heat equation with unknown right-hand side”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 3, 83–97; Russian Math. (Iz. VUZ), 65:3 (2021), 75–88
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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