In a domain with free boundary, we establish conditions for the existence and uniqueness of a solution of the inverse problem of finding the time-dependent coefficient of heat conductivity. We study the case of strong degeneration where the unknown coefficient tends to zero as t → +0 as a power function t β , where β ≥ 1.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 28–43, January, 2009.
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Hryntsiv, N.M., Ivanchov, M.I. Inverse problem for the strongly degenerate heat equation in a domain with free boundary. Ukr Math J 61, 30–49 (2009). https://doi.org/10.1007/s11253-009-0201-5
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DOI: https://doi.org/10.1007/s11253-009-0201-5