Geodesic
On the reconstruction of solutions of the Cauchy problem for the singular heat equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 231 (2024), pp. 89-99

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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, extremal problem, heat equation
Mots-clés : optimal reconstruction, Fourier–Bessel transform 
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     author = {M. V. Polovinkina},
     title = {On the reconstruction of solutions of the {Cauchy} problem for the singular heat equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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M. V. Polovinkina. On the reconstruction of solutions of the Cauchy problem for the singular heat equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 231 (2024), pp. 89-99. http://geodesic.mathdoc.fr/item/INTO_2024_231_a8/