Estimates of homogenization for a parabolic equation with periodic coefficients

The asymptotic behavior of the operator exponent related to the Cauchy problem for a parabolic equation with periodic coefficients is studied either under the reduction of the periodicity cell or for large times. Estimates for the closeness of the operator exponentials (the original and the limit) with respect to the L ²-operator norm and the related H ¹-estimates are obtained under minimal assumptions concerning the smoothness of the heat matrix and of the initial data. Financially supported by RFBR under grant no. 05-01-00621.