Homogenization of a parabolic operator with Signorini boundary conditions in perforated domains

The paper deals with homogenization of initial value problems for the standard parabolic equation in a periodically or randomly perforated domain. The boundary of the domain is assumed to be semi-permeable, and this implies Signorini boundary conditions for the sought variable. Convergence of solutions to the solution of the homogenized problem is proved under the minimal number of assumptions with respect to regularity of initial data and geometry of the boundaries.