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

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)

SN - 0272-4960

IS - 6

ER -