Compactness theorems for problems with unknown boundary
A. G. Podgaev, T. D. Kulesh
Pacific National University, Khabarovsk
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 $W_2^1$.
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.
Stefan's problems, quasilinear parabolic equation, non-cylindrical domain, compactness theorem.
PDF file (506 kB)
MSC: Primary 80A22; Secondary 35K55, 46N20
A. G. Podgaev, T. D. Kulesh, “Compactness theorems for problems with unknown boundary”, Dal'nevost. Mat. Zh., 21:1 (2021), 105–112
Citation in format AMSBIB
\by A.~G.~Podgaev, T.~D.~Kulesh
\paper Compactness theorems for problems with unknown boundary
\jour Dal'nevost. Mat. Zh.
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