Inverse problem for the strongly degenerate heat equation in a domain with free boundary - Ivanchov, N. I.; Hryntsiv, N. M. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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 $β ≥ 1$.