L²-Estimates of Error in Homogenization of Parabolic Equations with Correctors Taken Into Account

We consider second-order parabolic equations with bounded measurable ε-periodic coefficients. To solve the Cauchy problem in the layer ℝ^d × (0, T) with the nonhomogeneous equation, we obtain approximations in the norm \({\Vert \bullet \Vert }_{{L}^{2}\left({\mathbb{R}}^{d}\times \left(0,T\right)\right)}\) ${\Vert \bullet \Vert }_{L^2\left({\mathbb{R}}^d,\times ,\left(0,,,T\right)\right)}$ with remainder of order ε² as ε → 0.