Inverse problem for the strongly degenerate heat equation in a domain with free boundary

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. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 28–43, January, 2009.