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 $\epsilon$, 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.

20 pages. arXiv admin note: text overlap with arXiv:1912.02445, arXiv:1712.01183, arXiv:2004.06513

References in corpus (2)

• Coleman-Gurtin type equations with dynamic boundary conditions
• Reaction-diffusion equation on thin porous media

Cited by in corpus (1)

• Sharp pressure estimates for the Navier-Stokes system in thin porous media