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Solving Inverse Source Problems Using Observability. Applications to the Euler–Bernoulli Plate Equation
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History
Submitted: 29 May 2008
Accepted: 27 January 2009
Published online: 07 May 2009
Publication Data
ISSN (print): 0363-0129
ISSN (online): 1095-7138
CODEN: sjcodc
The aim of this paper is to provide a general framework for solving a class of inverse source problems by using exact observability of infinite dimensional systems. More precisely, we show that if a system is exactly observable, then a source term in this system can be identified by knowing its intensity and appropriate observations which often correspond to measurements of some boundary traces. This abstract theory is then applied to obtain new identifiability results for a system governed by the Euler–Bernoulli plate equation. Using a different methodology, we show that exact observability can be used to identify both the locations and the intensities of combinations of point sources in the plate equation.
Copyright © 2009 Society for Industrial and Applied Mathematics
Permalink: https://doi.org/10.1137/080725635
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