Homogenization of the Semi-linear Parabolic Problem in a Perforated Cylinder

For a second-order semi-linear parabolic equation with the lowest term growing in an unknown function in a power-law manner, we prove that the sequence of solutions of a mixed problem in a perforated cylinder tends to the solution of the same problem in a non-perforated cylinder if the radii of the ejected balls, in the parabolic metric, tend to zero at a rate depending on the exponent in the lowest term.