Geodesic
On the spectrum of the~pencil in the~Verigin--Muskat problem
Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 33-73

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Sufficient conditions close to necessary are obtained for the existence of a`classical solution of the Verigin–Muskat contact problem with a free boundary on a small time interval. Solvability conditions are obtained in terms of the spectrum of model parabolic initial-boundary value problems in a dihedral angle that contain the time derivative in the boundary condition. 
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     author = {E. V. Radkevich},
     title = {On the spectrum of the~pencil in {the~Verigin--Muskat} problem},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_1_a2/}
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E. V. Radkevich. On the spectrum of the~pencil in the~Verigin--Muskat problem. Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 33-73. http://geodesic.mathdoc.fr/item/SM_1995_80_1_a2/