# American Institute of Mathematical Sciences

July  2017, 37(7): 3625-3699. doi: 10.3934/dcds.2017156

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

 Institute of Applied Mathematics and Mechanics NASU, State Institute of Applied Mathematics and Mechanics, R.Luxemburg Str., 74, Donetsk, 83114, Ukraine

Received  November 2015 Revised  February 2017 Published  April 2017

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.

Citation: Sergey Degtyarev. Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3625-3699. doi: 10.3934/dcds.2017156
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