Reiterated deterministic homogenization problem for nonlinear pseudo monotone
parabolic type operators is considered beyond the usual periodic setting. We present
a new approach based on the generalized Besicovitch type spaces, which allows to
consider general assumptions on the coefficients of the operators under consideration.
In particular we solve the weakly almost periodic homogenization problem and many
new other problems such as the homogenization in the Fourier-Stieltjes algebra. Our
approach falls within the scope of multiscale convergence method.