On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media

Abstract

This paper deals with the homogenization of the $p$-Laplacian reaction-diffusion problems in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of pure-reactive type. We generalize our previous results established in the case where the diffusion is modeled by the Laplacian operator, i.e., with $p=2$. We prove the convergence of the homogenization process to a nonlinear $p$-Laplacian reaction-diffusion equation defined on a unified domain without holes with zero Dirichlet boundary condition and with extra terms coming from the influence of the nonlinear dynamical boundary conditions.