B. V. Bazaliy, S. P. Degtyarev, “Classical solution of a degenerate elliptic-parabolic free boundary problem”, Zh. Mat. Fiz. Anal. Geom., 2011, Volume 7, Number 4,Pages <nobr>295

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Classical solution of a degenerate elliptic-parabolic free boundary problem

B. V. Bazaliy, S. P. Degtyarev

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 74 R. Luxemburg Str., Donetsk 83114, Ukraine

Abstract: A free boundary problem describing a filtration process in a porous medium is considered. An unknown interface divides the filtration domain into elliptic and parabolic regions. In the parabolic region the governing equation is degenerate. The existence of a smooth solution in the weighted Hölder space is proved

Key words and phrases: elliptic and parabolic equations, free boundary problems, classical solutions, a priori estimates.

MSC: 35K65, 35R35

Received: 11.03.2011

Language: English