| Abstract: | In this paper, we study, via variational methods, the problem of scattering
of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound
soft rough surface. We first propose a variational formulation and exploit it as a
theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which
exhibit explicitly dependence of bound on the wave number and on the geometry of
the domain. Then, based on the non-absorbing results, we show that the variational
problem remains uniquely solvable when the layer is absorbing by means of a priori
estimate of the solution. Finally, we consider the finite element approximation of the
problem and give an error estimate. |
