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In L 2 (ℝd ; ℂn ), we consider a wide class of matrix elliptic second order differential operators $\mathcal{A}$e with rapidly oscillating coefficients (depending on x /e ). For a fixed τ > 0 and small e > 0, we find approximation of the operator exponential exp(− $\mathcal{A}$e τ ) in the (L 2 (ℝd ; ℂn ) → H 1 (ℝd ; ℂn ))-operator norm with an error term of order e . In this approximation, the corrector is taken into account. The results are applied to homogenization of a periodic parabolic Cauchy problem.

Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev SpaceH1(ℝd)

Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev SpaceH¹(ℝ^d)