2019
Том 71
№ 9

# Hryntsiv N. M.

Articles: 2
Article (Ukrainian)

### Stefan problem for a weakly degenerate parabolic equation

Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 640-653

In a domain with free boundary, we consider the inverse problem for the determination of time dependent coefficient of the first derivative of unknown fonction in a parabolic equation with weak power degeneration. As overdetermination conditions, the Stefan condition and the integral condition are given. Conditions for the existence and uniqueness of the classical solution of considered problem are established.

Article (Ukrainian)

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

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 28-43

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 $β ≥ 1$.