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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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https://hal.archives-ouvertes.fr/hal-01224012
Contributor : Guillaume Olive <>
Submitted on : Tuesday, November 3, 2015 - 7:25:46 PM
Last modification on : Thursday, December 10, 2020 - 12:34:13 PM
Long-term archiving on: : Thursday, February 4, 2016 - 11:29:48 AM

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  • HAL Id : hal-01224012, version 1
  • ARXIV : 1511.01078

Citation

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

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