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The paper deals with periodic homogenization problem for a para\-bo\-licequation whose elliptic part is a convolution type operator with rapidlyoscillating coefficients. It is assumed that the coefficients are rapidlyoscillating periodic functions both in spatial and temporal variables and thatthe scaling is diffusive that is the scaling factor of the temporal variable isequal to the square of the scaling factor of the spatial variable. Under theassumption that the convolution kernel has a finite second moment and that theoperator is symmetric in spatial variables we show that the studied equationadmits homogenization and prove that the limit operator is a second orderdifferential parabolic operator with constant coefficients.

Homogenization of non-autonomous operators of convolution type in periodic media