This article is cited in 1 paper

Compactness theorems for problems with unknown boundary

A. G. Podgaev, T. D. Kulesh

Pacific National University, Khabarovsk

Abstract: The compactness theorem is proved for sequences of functions that have estimates of the higher derivatives in each subdomain of the domain of definition, divided into parts by a sequence of some curves of class $W_2^1$. At the same time, in the entire domain of determining summable higher derivatives, these sequences do not have. These results allow us to make limit transitions using approximate solutions in problems with an unknown boundary that describe the processes of phase transitions.

Key words: Stefan's problems, quasilinear parabolic equation, non-cylindrical domain, compactness theorem.

UDC: 517.957

MSC: Primary 80A22; Secondary 35K55, 46N20

Received: 28.03.2021

DOI: 10.47910/FEMJ202109