Deterministic homogenization of parabolic monotone operators with time dependent coefficients

Abstract

We study, beyond the classical periodic setting, the homogenization of linear and nonlinear parabolic differential equations associated with monotone operators. The usual periodicity hypothesis is here substituted by an abstract deterministic assumption characterized by a great relaxation of the time behaviour. Our main tool is the recent theory of homogenization structures by the first author, and our homogenization approach falls under the two-scale convergence method. Various concrete examples are worked out with a view to pointing out the wide scope of our approach and bringing the role of homogenization structures to light.