The Helmholtz equation with impedance in a half-plane

Mario Durán; Ignacio Muga; Jean Claude Nédélec

doi:10.1016/j.crma.2005.02.015

The Helmholtz equation with impedance in a half-plane

Translated title of the contribution: The Helmholtz equation with impedance in a half-plane

Mario Durán, Ignacio Muga, Jean Claude Nédélec

INSTITUTE OF MATHEMATICS

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions.

Translated title of the contribution	The Helmholtz equation with impedance in a half-plane
Original language	English
Pages (from-to)	483-488
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	340
Issue number	7
DOIs	https://doi.org/10.1016/j.crma.2005.02.015
State	Published - 1 Apr 2005

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10.1016/j.crma.2005.02.015

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title = "The Helmholtz equation with impedance in a half-plane",

abstract = "This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions.",

author = "Mario Dur{\'a}n and Ignacio Muga and N{\'e}d{\'e}lec, {Jean Claude}",

note = "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, the DIM of the Universidad de Chile.",

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AU - Muga, Ignacio

AU - Nédélec, Jean Claude

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N2 - This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions.

AB - This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions.

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IS - 7

ER -

The Helmholtz equation with impedance in a half-plane

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