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Integral equation methods for scattering by infinite rough surfaces. (English) Zbl 1016.78006
In the paper under review, the authors consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane. These boundary value problems arise in the study of time-harmonic acoustic scattering of an incident field by a sound-soft, infinite rough surface where the total field vanishes (the Dirichlet problem) or by an infinite, impedance rough surface where the total field satisfies a homogeneous impedance condition (the impedance problem). They propose boundary integral equation formulations for these problems. It is proved that all the integral equations proposed are uniquely solvable in the space of bounded and continuous functions for all wavenumbers.

MSC:
78A45 Diffraction, scattering
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
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