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Journal Articles Journal of Functional Analysis Year : 2016

Stabilization and controllability of first-order integro-differential hyperbolic equations

Abstract

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prove the invertibility of such a transformation. Finally, using the method of moments, we show in a particular case that the controllability is reduced to the criterion of Fattorini.
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Dates and versions

hal-01224012 , version 1 (03-11-2015)

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Jean-Michel Coron, Long Hu, Guillaume Olive. Stabilization and controllability of first-order integro-differential hyperbolic equations. Journal of Functional Analysis, 2016, 271 (12). ⟨hal-01224012⟩
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