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A uniqueness result for scattering by infinite rough surfaces

Chandler-Wilde, S. N. 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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:32653
Publisher:Society for Industrial and Applied Mathematics

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