On homogenization of periodic parabolic systems

We study homogenization in the small period limit for a periodic parabolic Cauchy problem in ^d and prove that the solutions converge in L₂(^d) to the solution of the homogenized problem for each t > 0. For the L₂(^d)-norm of the difference, we obtain an order-sharp estimate uniform with respect to the L₂(^d)-norm of the initial value.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 86–90, 2004Original Russian Text Copyright © by T. A. SuslinaSupported by RFBR grant No. 02-01-00798.