Homogenization of Semilinear Elliptic and Parabolic Operators in Perforated Domains

A second order semi linear elliptic (parabolic) equation whose lower term has power-like growth at infinity with respect to the unknown function is considered. It is proved that a sequence of solutions in the perforated domains (cylinders) converges to a solution in the non-perforated domain (cylinder) as the diameters of the rejected balls (in parabolic metric) converge to zero with a rate depending on the power exponent of the lower term.