We study the inverse problem of recovering the source function in a degenerate parabolic equation with many spatial variables. An additional integral observation condition is imposed. We find sufficient conditions for the unique solvability of the inverse problem in the cases where the unknown source function is looked for in the space L2(0, T) or L∞(0, T). The results obtained are based on the preliminary study of the corresponding direct problem which are of independent interest.
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Translated from Problemy Matematicheskogo Analiza 120, 2023, pp. 35-49.
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Kamynin, V.L. Unique Solvability of Direct and Inverse Problems for Degenerate Parabolic Equations in the Multidimensional Case. J Math Sci 269, 36–52 (2023). https://doi.org/10.1007/s10958-023-06253-z
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DOI: https://doi.org/10.1007/s10958-023-06253-z