The Helmholtz Equation in a Locally Perturbed Half-Space with Non-Absorbing Boundary
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Date
2009
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Abstract
We obtain uniqueness and existence results of an outgoing solution for the Helmholtz equation in a half-space, or in a compact local perturbation of it, with an impedance boundary condition. It is worth noting that these kinds of domains have unbounded boundaries which lead to a non-classical exterior problem. The established radiation condition is somewhat different from the usual Sommerfeld's one, due to the appearance of surface waves (in the case of a non-absorbing boundary). A half-space Green's function framework is used to carry out our computations. This is an extended and detailed version of the previous article "The Helmholtz equation with impedance in a half-space," Duran et al. (CR Acad Sci Paris Ser I 341:561-566, 2005).