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Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media (1712.01183v1)
Published 4 Dec 2017 in math.AP
Abstract: We consider a nonlinear parabolic problem with dynamical boundary conditions in a media perforated by periodically distributed holes of size $\varepsilon$. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when $\varepsilon$ goes to zero, a new nonlinear parabolic problem defined on a unified domain without holes with zero Dirichlet boundary condition and with extra-terms coming from the influence of the dynamical boundary conditions is rigorously derived.