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Well-posedness and stability results for a quasilinear periodic Muskat problem

Matioc, Anca-Voichita ; Matioc, Bogdan-Vasile



Abstract

We study the Muskat problem describing the spatially periodic motion of two fluids with equal viscosities under the effect of gravity in a vertical unbounded two-dimensional geometry. We first prove that the classical formulation of the problem is equivalent to a nonlocal and nonlinear evolution equation expressed in terms of singular integrals and having only the interface between the fluids as ...

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