Higher-Order Approximations of the Averaging Method for Parabolic Initial-Boundary Value Problems with Rapidly Oscillating Coefficients.

The article presents a discourse on higher-order approximations of the averaging method for Parabolic Initial-Boundary Value Problems with Rapidly Oscillating Coefficients. For abstract parabolic equations with initial conditions and for semi-linear parabolic initial boundary value problems whose coefficients rapidly change in the course of time, it was shown in a previous article that the solution of the averaged problem is an asymptotic approximation (in certain norms) to the solution of the original (perturbed) problem.