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The paper is devoted to studying a viscous thin-film equation with a singular diffusion term and the periodic boundary conditions in multidimensional space, which has a lot of applications in fluids theory such as draining of foams and the movement of contact lenses. In order to obtain the necessary uniform estimates and overcome the difficulty of a singular diffusion term, the entropy functional method is used. Finally, the existence of nonnegative weak solutions is obtained by some compactness arguments.

A viscous thin-film equation with a singular diffusion