Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces (Communications in Mathematical Research, 2021)
In this paper, we study, via variational methods, the problem of scatteringof time harmonic acoustic waves by unbounded inhomogeneous layers above a soundsoft rough surface. We first propose a variational formulation and exploit it as atheoretical 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, whichexhibit explicitly dependence of bound on the wave number and on the geometry ofthe domain. Then, based on the non-absorbing results, we show that the variationalproblem remains uniquely solvable when the layer is absorbing by means of a prioriestimate of the solution. Finally, we consider the finite element approximation of theproblem and give an error estimate.
Keywords: Helmholtz equation; rough surface; scattering problem.