On the spectrum of the pencil in the Verigin–Muskat problem

E. V. Radkevich

Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 33-73

Résumé

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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