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Solving inverse source problems using observability. Applications to the Euler-Bernoulli plate equation

Carlos Alves 1, Ana Leonor Silvestre 1, Takéo Takahashi 2, 3, Marius Tucsnak 2, 3

(29/05/2008)

The aim of this paper is to provide a general framework allowing to use exact observability of infinite dimensional systems to solve a class of inverse source problems. More precisely, we show that if a system is exactly observable, then we can identify a source term in this system by knowing the corresponding intensity and appropriate observations which often correspond to the measure of some boundary traces. This abstract theory is then applied to 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.

1 :	Instituto Superior Técnico
	Instituto Superior Tecnico de Lisboa
2 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine
3 :	CORIDA (INRIA Lorraine / IECN / MMAS)
	INRIA – CNRS : UMR7122 – CNRS : UMR7502 – Université Paul Verlaine - Metz – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine

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Mathématiques/Equations aux dérivées partielles

hal-00283402, version 1

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Contributeur : Takéo Takahashi <>

Soumis le : Jeudi 29 Mai 2008, 18:36:07

Dernière modification le : Jeudi 29 Mai 2008, 20:22:20