Two-Scale Convergence Method and Scattering Problems

In this paper, we deal with the steady-state acoustic wave equation in the space ℝ 3 diffracted by an obstacle made by an inhomogeneous medium and located in a bounded domain. The inhomogeneity of the medium depends on a parameter ε > 0. If the solution u ε converges to a solution u 0 of the limit problem as ε → 0, as in the homogenization process, then we can use the two-scale convergence method to study the convergence of the gradient.