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

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 and Ross, C. R. (1999) Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium. Inverse Problems, 11 (5). pp. 1063-1067. ISSN 1361-6420 doi: 10.1088/0266-5611/11/5/010

Abstract/Summary

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.