Averaging Differential Operators With Almost Periodic, Rapidly Oscillating Coefficients

The Dirichlet problem containing a small parameter is considered, where the coefficients are almost periodic functions in the sense of Besicovitch. An averaged equation having constant coefficients is contracted, and the convergence of to the solution of the averaged equation is proved. An estimate of the remainder is obtained under the condition that there are no anomalous commensurable frequencies in the spectrum of the coefficients. For the problem in the whole space a complete asymptotic expansion in powers of is constructed.Bibliography: 12 titles.