Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

Abstract

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Delta u+ kappa 2u=0, with Im kappa >0, in an arbitrary bounded or unbounded open set G contained in/implied by Rn. Assuming continuity of the solution up to the boundary and a bound on growth at infinity, that mod u(x) mod <or=Cexp( theta mod x mod ), for some C>0 and theta <Im kappa , we prove that the homogeneous problem has only the trivial solution. With this result we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.