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Scattering by rough surfaces: The Dirichlet problem for the Helmholtz equation in a nonlocally perturbed half-plane. (English) Zbl 0863.35032
The Dirichlet boundary value problem for the Helmholtz equation is considered in a non-locally perturbed half-plane, the origins of the problem being in the scattering by one-dimensional rough perfectly conducting surfaces. A new boundary integral formulation is proposed utilizing the Green’s function for an impendance half-plane in place of the standard fundamental solution. The problem is shown to have a unique bounded and continuous solution. The continuous dependence of the solution on the boundary shape is also established.

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
35C15 Integral representations of solutions to PDEs
Full Text: DOI
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