Reconstruction of a nonlinear source term in a semi-linear wave equation
(2002) In Technical Report LUTEDX/(TEAT-7108)/1-28/(2002)- Abstract
- An inverse source problem associated with a semi-linear transport or one-way wave equation in one
spatial dimension is considered. It is shown an analytic solution to the inverse problem can be
given and furthermore, that this inverse problem of determination of a source function is
ill-posed, and must be regularised. A novel regularisation scheme which combines least squares
monotone approximation and mollification of the noisy data is used to provide this regularisation.
Proof of convergence of this regularisation scheme of \emph{monotone smoothing} is given. Numerical
solutions from the inverse problems are presented showing that the method is robust to noisy
... (More) - An inverse source problem associated with a semi-linear transport or one-way wave equation in one
spatial dimension is considered. It is shown an analytic solution to the inverse problem can be
given and furthermore, that this inverse problem of determination of a source function is
ill-posed, and must be regularised. A novel regularisation scheme which combines least squares
monotone approximation and mollification of the noisy data is used to provide this regularisation.
Proof of convergence of this regularisation scheme of \emph{monotone smoothing} is given. Numerical
solutions from the inverse problems are presented showing that the method is robust to noisy
signals.
The solution of this inverse problem is also shown to illustrate the behaviour of more complex
problems from electromagnetism and nonlinear optics. The mathematical techniques that are developed
are therefore applicable to other sets of nonlinear first order equations. The method is therefore
model independent. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1782326
- author
- Connolly, John and Wall, David LU
- organization
- publishing date
- 2002
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7108)/1-28/(2002)
- pages
- 28 pages
- publisher
- [Publisher information missing]
- report number
- TEAT-7108
- language
- English
- LU publication?
- yes
- id
- 51157664-2d6a-4e47-890e-b07b48691315 (old id 1782326)
- date added to LUP
- 2016-04-04 13:03:37
- date last changed
- 2018-11-21 21:12:00
@techreport{51157664-2d6a-4e47-890e-b07b48691315,
abstract = {{An inverse source problem associated with a semi-linear transport or one-way wave equation in one<br/><br>
spatial dimension is considered. It is shown an analytic solution to the inverse problem can be<br/><br>
given and furthermore, that this inverse problem of determination of a source function is<br/><br>
ill-posed, and must be regularised. A novel regularisation scheme which combines least squares<br/><br>
monotone approximation and mollification of the noisy data is used to provide this regularisation.<br/><br>
Proof of convergence of this regularisation scheme of \emph{monotone smoothing} is given. Numerical<br/><br>
solutions from the inverse problems are presented showing that the method is robust to noisy<br/><br>
signals.<br/><br>
<br/><br>
The solution of this inverse problem is also shown to illustrate the behaviour of more complex<br/><br>
problems from electromagnetism and nonlinear optics. The mathematical techniques that are developed<br/><br>
are therefore applicable to other sets of nonlinear first order equations. The method is therefore<br/><br>
model independent.}},
author = {{Connolly, John and Wall, David}},
institution = {{[Publisher information missing]}},
language = {{eng}},
number = {{TEAT-7108}},
series = {{Technical Report LUTEDX/(TEAT-7108)/1-28/(2002)}},
title = {{Reconstruction of a nonlinear source term in a semi-linear wave equation}},
url = {{https://lup.lub.lu.se/search/files/6045013/1782328.pdf}},
year = {{2002}},
}