We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. Chandler-Wilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

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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 0 and theta

The vein diagram is a new method of visualizing the time-frequency characteristics of acoutic signals [Yen et al., J. Acoust. Soc. Am. 87, 2359–2370 (1990)]. It is based on the modified Wigner distribution function. Previously this technique has been used for analysis of acoustic scattering including the inverse scattering problem. Here, the vein diagram, is employed as a visualization tool to display the effect of a surface mounted projector on acoustic scattering from a submerged complex structure. The projector is part of an active vibration control system. The important feature of this technique is that is allows distinct observation of the influence of the control signal on each of the various types of structural vibrations.