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Reconstruction of a nonlinear source term in a semi-linear wave equation

Connolly, John and Wall, David LU (2002) In Technical Report LUTEDX/(TEAT-7108)/1-28/(2002) TEAT-7108.
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)
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Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7108)/1-28/(2002)
volume
TEAT-7108
pages
28 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
51157664-2d6a-4e47-890e-b07b48691315 (old id 1782326)
date added to LUP
2011-02-04 12:24:38
date last changed
2016-04-16 10:47:09
@misc{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},
  language     = {eng},
  pages        = {28},
  publisher    = {ARRAY(0x9302678)},
  series       = {Technical Report LUTEDX/(TEAT-7108)/1-28/(2002)},
  title        = {Reconstruction of a nonlinear source term in a semi-linear wave equation},
  volume       = {TEAT-7108},
  year         = {2002},
}