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

摘要

The paper deals with homogenization problem for nonlinear elliptic andparabolic equations in a periodically perforated domain, a nonlinear Fourierboundary conditions being imposed on the perforation border. Under theassumptions that the studied differential equation satisfies monotonicity and2-growth conditions and that the coefficient of the boundary operator iscentered at each level set of unknown function, we show that the problem underconsideration admits homogenization and derive the effective model.