Variational method of scattering by inhomogeneous anisotropic layers

In this paper, we studied the problem of scattering of time harmonic acoustic waves by an inhomogeneous anisotropic layers above a sound soft rough surface. We proved first, via variational methods, the well-posedness of this problem when the wave number is small enough for the non-absorbing case, and obtained a stability estimate about solution, which exhibits the explicit dependence of bound on the wave number and the geometry of the domain. Then we analyzed the absorbing case and showed the well-posedness by means of a priori estimate of solutions based on the non-absorbing results.