Space-time homogenization for nonlinear diffusion

The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations periodically oscillating (in space and time) coefficients. Main results consist of theorem (i.e., convergence solutions as the period oscillation goes to zero) well characterization homogenized equations. In particular, matrices are described in terms cell-problems, which have different forms depending on log-ratio spatial temporal periods At critical ratio, cell turns out be parabolic equation microscopic variables (as linear diffusion) also involves limit solutions, function macroscopic variables. latter feature stems from nonlinearity equation, moreover, some strong interplay between structures can explicitly seen diffusion. As other ratios, problems always elliptic micro-variable only) do not involve any variables, hence, micro- macrostructures weakly interacting each other. Proofs main based two-scale theory (for homogenization). Furthermore, finer asymptotics gradients, fluxes time-derivatives certain corrector provided, qualitative analysis performed.