M. V. Polovinkina, “On the reconstruction of solutions of the Cauchy problem for the singular heat equation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2024, Volume 231,Pages <nobr>89

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

M. V. Polovinkina

Voronezh State University of Engineering Technologies

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

UDC: 517.9

MSC: 26A33, 35Q92, 35B40, 43A32, 35J15

DOI: 10.36535/2782-4438-2024-231-89-99