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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2009

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

Résumé

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.
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Dates et versions

hal-00283402 , version 1 (29-05-2008)

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Carlos Alves, Ana Leonor Silvestre, Takéo Takahashi, Marius Tucsnak. Solving inverse source problems using observability. Applications to the Euler-Bernoulli plate equation. SIAM Journal on Control and Optimization, 2009, 48 (3), pp.1632-1659. ⟨10.1137/080725635⟩. ⟨hal-00283402⟩
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