Geodesic
On some classes of inverse parabolic problems of recovering the thermophysical parameters
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 3, pp. 23-33

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In the article we examine the question of regular solvability in Sobolev spaces of parabolic inverse coefficient problems. A solution is sought in the class of regular solutions that has all derivatives occurring in the equation summable to some power. The overdetermination conditions are the values of a solution at some collection of points lying inside the domain. The proof is based on a priori estimates and the fixed point theorem.
Keywords: inverse problem, initial-boundary value problem, uniqueness.
Mots-clés : parabolic equation, existence 
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     title = {On some classes of inverse parabolic problems of recovering the thermophysical parameters},
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S. G. Pyatkov; O. A. Soldatov. On some classes of inverse parabolic problems of recovering the thermophysical parameters. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 3, pp. 23-33. http://geodesic.mathdoc.fr/item/VYURM_2023_15_3_a2/