TY - JOUR
T1 - The Helmholtz equation in a locally perturbed half-plane with passive boundary
AU - Durán, Mario
AU - Muga, Ignacio
AU - Nédélec, Jean Claude
N1 - Funding Information:
This work was supported by the Fondecyt Project No. 1030480, the Évaluation-orientation de la Coopération Scientifique/Conicyt Project No. C03–E08 and the Conicyt fellowship for doctoral student. Ignacio Muga wants to thank particularly the Departamento de Ingeniería Matemática of Universidad de Chile and CMAP of the École Polytechnique.
PY - 2006/12
Y1 - 2006/12
N2 - In this article, we study the existence and uniqueness of outgoing solutions for the Helmholtz equation in locally perturbed half-planes with passive boundary. We establish an explicit outgoing radiation condition which is somewhat different from the usual Sommerfeld's one due to the appearance of surface waves. We work with the help of Fourier analysis and a half-plane Green's function framework. This is an extended and detailed version of the previous article Durán et al. (2005, The Helmholtz equation with impedance in a half-plane. C. R. Acad. Sci. Paris, Ser. I, 340, 483-488).
AB - In this article, we study the existence and uniqueness of outgoing solutions for the Helmholtz equation in locally perturbed half-planes with passive boundary. We establish an explicit outgoing radiation condition which is somewhat different from the usual Sommerfeld's one due to the appearance of surface waves. We work with the help of Fourier analysis and a half-plane Green's function framework. This is an extended and detailed version of the previous article Durán et al. (2005, The Helmholtz equation with impedance in a half-plane. C. R. Acad. Sci. Paris, Ser. I, 340, 483-488).
KW - Green's function
KW - Helmholtz equation on half-plane
KW - Radition condition
UR - http://www.scopus.com/inward/record.url?scp=33845399652&partnerID=8YFLogxK
U2 - 10.1093/imamat/hxl023
DO - 10.1093/imamat/hxl023
M3 - Article
AN - SCOPUS:33845399652
SN - 0272-4960
VL - 71
SP - 853
EP - 876
JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
IS - 6
ER -