The Helmholtz equation with impedance in a half-plane
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Date
2005
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ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Abstract
This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.