Narrow Results

Using the two-scale convergence method, we study the asymptotic behavior of a wave problem in ℝ^N with periodic coefficients in the space variable and almost-periodic coefficients in the time one. We obtain a nonlocal corrector and show how this implies that the limit problem is nonlocal in general.

For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the asymptotic almost periodic setting, and we show that the rates of convergence for the zero-order approximation, are near optimal. The results obtained constitute a step towards the numerical implementation of results from the deterministic homogenization theory beyond the periodic setting. To illustrate this, numerical simulations based on finite volume method are provided to sustain our theoretical results.