TY - JOUR

T1 - The Helmholtz equation with impedance in a half-space

AU - Durán, Mario

AU - Muga, Ignacio

AU - Nédélec, Jean Claude

N1 - Funding Information:
This work was supported by the Fondecyt Project #1030480, the ECOS/Conicyt Project #C03-E08 and the Conicyt fellowship for doctorate students. Ignacio Muga wants to thank particularly to the DIM of the Universidad de Chile.

PY - 2005/11/1

Y1 - 2005/11/1

N2 - In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ℝ+ 3 with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data.

AB - In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ℝ+ 3 with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data.

UR - http://www.scopus.com/inward/record.url?scp=27744578335&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2005.09.021

DO - 10.1016/j.crma.2005.09.021

M3 - Article

AN - SCOPUS:27744578335

SN - 1631-073X

VL - 341

SP - 561

EP - 566

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -