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A uniqueness theorem for the Helmholtz' equation: Penetrable media with an infinite interface

Kristensson, Gerhard LU (1980) In SIAM Journal on Mathematical Analysis 11(6). p.1104-1117
Abstract
In this paper we will prove the uniqueness of a solution to Helmholtz' equation for two halfspaces of different media in $n$ dimensions. The theorem allows a finite number of bounded inhomogeneities in each half space. The surface separating the half spaces is assumed to be a cone of arbitrary cross section far away from the origin and is furthermore assumed to be smooth. We assume all space to be lossless, and in each halfspace we assume a radiation condition to be fulfilled. The boundary conditions at the interface are a general coupling in the field and its normal derivative with constant coefficients.
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Mathematical Analysis
volume
11
issue
6
pages
1104 - 1117
publisher
SIAM
ISSN
0036-1410
DOI
10.1137/0511096
language
English
LU publication?
no
id
da679302-2949-413c-a66c-104caae8a4d8 (old id 1041179)
date added to LUP
2008-03-03 12:31:36
date last changed
2016-06-29 09:14:43
@article{da679302-2949-413c-a66c-104caae8a4d8,
  abstract     = {In this paper we will prove the uniqueness of a solution to Helmholtz' equation for two halfspaces of different media in $n$ dimensions. The theorem allows a finite number of bounded inhomogeneities in each half space. The surface separating the half spaces is assumed to be a cone of arbitrary cross section far away from the origin and is furthermore assumed to be smooth. We assume all space to be lossless, and in each halfspace we assume a radiation condition to be fulfilled. The boundary conditions at the interface are a general coupling in the field and its normal derivative with constant coefficients.},
  author       = {Kristensson, Gerhard},
  issn         = {0036-1410},
  language     = {eng},
  number       = {6},
  pages        = {1104--1117},
  publisher    = {SIAM},
  series       = {SIAM Journal on Mathematical Analysis},
  title        = {A uniqueness theorem for the Helmholtz' equation: Penetrable media with an infinite interface},
  url          = {http://dx.doi.org/10.1137/0511096},
  volume       = {11},
  year         = {1980},
}