$\sum $-convergence and reiterated homogenization of nonlinear parabolicoperators

We study the reiterated homogenization of nonlinear parabolic differentialequations associated with monotone operators. Contrary to what is usuallydone in the deterministic homogenization theory, we present a new approachbased on a deterministic assumption on the coefficients of the operators,which allows us to consider the concrete homogenization problems from a trueand natural perspective, taking into account the discontinuities in general.Based on this new approach we obtain very general homogenization results,and we solve several concrete homogenization problems. Our main tool is thetheory of homogenization structures, and our homogenization approach fallswithin the scope of multiscale convergence method.