The Helmholtz Equation in a Locally Perturbed Half-Space with Non-Absorbing Boundary

Resumen

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)

Autores: Durán, M., Muga, I., Nédélec, J-C.

Journal: Archive for Rational Mechanics and Analysis

Journal Volume: 191

Journal Issue: 1

Journal Page: 143-172

Tipo de publicación: ISI

Fecha de publicación: 2009

Topics:

DOI: 10.1007/s00205-008-0135-3

URL de la publicación: http://link.springer.com/article/10.1007%2Fs00205-008-0135-3