A uniqueness result for scattering by infinite rough surfaces

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 and Zhang, B. (1998) A uniqueness result for scattering by infinite rough surfaces. SIAM Journal on Applied Mathematics (SIAP), 58 (6). pp. 1774-1790. ISSN 0036-1399 doi: 10.1137/S0036139996309722

Abstract/Summary

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/32653
Identification Number/DOI	10.1137/S0036139996309722
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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