A uniqueness theorem for the Helmholtz' equation: Penetrable media with an infinite interface
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1041179
- author
- Kristensson, Gerhard LU
- publishing date
- 1980
- type
- Contribution to journal
- publication status
- published
- subject
- in
- SIAM Journal on Mathematical Analysis
- volume
- 11
- issue
- 6
- pages
- 1104 - 1117
- publisher
- Society for Industrial and Applied Mathematics
- 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
- 2016-04-04 09:43:55
- date last changed
- 2020-02-26 15:00:53
@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 = {{Society for Industrial and Applied Mathematics}}, 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}}, doi = {{10.1137/0511096}}, volume = {{11}}, year = {{1980}}, }