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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.

MSC:
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
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