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Existence and construction of solutions of dissipative inverse problems

Kristensson, Gerhard LU ; Krueger, Robert J and Winther, Ronald C (1991) In Journal of Mathematical Analysis and Applications 157(2). p.542-554
Abstract
The problem considered here is that of simultaneously reconstructing spatially dependent velocity and dissipation profiles for a one-dimensional medium using a finite time trace of normal incidence reflection data measured on one side of the medium. It is shown that if the sup norm of the reflection data is bounded in a particular way, then this inverse problem is guaranteed to have a solution. A numerical algorithm which is based on this existence proof is used to illustrate the reconstruction process.
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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Analysis and Applications
volume
157
issue
2
pages
542 - 554
publisher
Academic Press
external identifiers
  • scopus:5544262883
ISSN
0022-247X
DOI
10.1016/0022-247X(91)90105-9
language
English
LU publication?
no
id
c2a08b5f-b5ff-4812-8f25-5794cb7d0cec (old id 1038987)
date added to LUP
2016-04-04 09:35:21
date last changed
2025-10-14 10:12:23
@article{c2a08b5f-b5ff-4812-8f25-5794cb7d0cec,
  abstract     = {{The problem considered here is that of simultaneously reconstructing spatially dependent velocity and dissipation profiles for a one-dimensional medium using a finite time trace of normal incidence reflection data measured on one side of the medium. It is shown that if the sup norm of the reflection data is bounded in a particular way, then this inverse problem is guaranteed to have a solution. A numerical algorithm which is based on this existence proof is used to illustrate the reconstruction process.}},
  author       = {{Kristensson, Gerhard and Krueger, Robert J and Winther, Ronald C}},
  issn         = {{0022-247X}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{542--554}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{Existence and construction of solutions of dissipative inverse problems}},
  url          = {{http://dx.doi.org/10.1016/0022-247X(91)90105-9}},
  doi          = {{10.1016/0022-247X(91)90105-9}},
  volume       = {{157}},
  year         = {{1991}},
}