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

Abstract

We study the effect of the p-Laplacian operator in the modelling of the heat equation through a porous medium ( ). The case of was recently published in Anguiano (Mediterr J Math 17:18, https://doi.org/10.1007/s00009-019-1459-y, 2020). Using rigorous functional analysis techniques and the properties of Sobolev spaces, we managed to solve additional (nontrivial) difficulties which arise compared to the study for , and we prove a convergence theorem in appropriate functional spaces.