Homogenization of semilinear parabolic equations in perforated domains

This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated by epsilon-periodic holes of size epsilon. A Neumann condition is prescribed on the boundary of the holes. The presence of the holes does not allow to prove a compactness of the solutions in L-2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as epsilon --> 0 is described, and the limit equation is given.