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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 231, Pages 89–99
DOI: https://doi.org/10.36535/2782-4438-2024-231-89-99 (Mi into1257) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the reconstruction of solutions of the Cauchy problem for the singular heat equation

M. V. Polovinkina

Voronezh State University of Engineering Technologies
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DOI: https://doi.org/10.36535/2782-4438-2024-231-89-99
Abstract: The problem of reconstructing solutions of the singular heat equation on the positive part of the real axis at a certain moment of time is solved by inaccurate measurements of this solution at other previous moments of time. Explicit expressions for the optimal reconstruction method and its errors are obtained.
Keywords: Bessel operator, optimal reconstruction, extremal problem, Fourier–Bessel transform, heat equation
Document Type: Article
UDC: 517.9
MSC: 26A33, 35Q92, 35B40, 43A32, 35J15
Language: Russian
Citation: M. V. Polovinkina, “On the reconstruction of solutions of the Cauchy problem for the singular heat equation”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 231, VINITI, Moscow, 2024, 89–99
Citation in format AMSBIB
\Bibitem{Pol24}
\by M.~V.~Polovinkina
\paper On the reconstruction of solutions of the Cauchy problem for the singular heat equation
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 231
\pages 89--99
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1257}
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