Averaging of nonstationary parabolic operators with large lower order terms

In this note we study the homogenization problem for a singularly perturbed non-stationary parabolic operator with lower order terms. We assume a self-similar scaling of spatial and temporal variables and prove the existence of rapidly moving coordinates in which a solution of the corresponding Cauchy problem is asymptotically given as the product of the ground state of periodic cell problem and a solution of parabolic equation with constant coefficients.