Classical Solution of a Degenerate Elliptic-Parabolic Free Boundary Problem - Bazaliy, B.V.; Degtyarev, S.P. (Журнал математической физики, анализа, геометрии, 2011)
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 Holder space is proved.