Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of Fourier type

TL;DR

This paper investigates the homogenization of nonlinear elliptic and parabolic equations with Fourier boundary conditions in perforated domains, deriving an effective model under monotonicity and oscillating boundary conditions.

Contribution

It introduces a homogenization framework for nonlinear PDEs with Fourier boundary conditions in perforated domains, including the derivation of the effective model.

Findings

Homogenization is valid under monotonicity and 2-growth conditions.

Effective model derived for nonlinear equations with oscillating boundary conditions.

Boundary operator coefficients are centered at each level set of the unknown function.

Abstract

The paper deals with homogenization problem for nonlinear elliptic and parabolic equations in a periodically perforated domain, a nonlinear Fourier boundary conditions being imposed on the perforation border. Under the assumptions that the studied differential equation satisfies monotonicity and 2-growth conditions and that the coefficient of the boundary operator is centered at each level set of unknown function, we show that the problem under consideration admits homogenization and derive the effective model.