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Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting

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  • We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation with the mobility n = 2 in the case of partial wetting. We also obtain the Schauder estimates and solvability for the Dirichlet and the Neumann problem for a linear degenerate parabolic equation of fourth order.

    Mathematics Subject Classification: Primary: 35R35, 35K55; Secondary: 35K65.

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