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We consider a nonlinear parabolic problem with dynamical boundary conditionsin a media perforated by periodically distributed holes of size $\varepsilon$.The existence and uniqueness of solution is analyzed. Moreover, passing to thelimit when $\varepsilon$ goes to zero, a new nonlinear parabolic problemdefined on a unified domain without holes with zero Dirichlet boundarycondition and with extra-terms coming from the influence of the dynamicalboundary conditions is rigorously derived.

Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media