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Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping

Abstract : In this paper, we study input-to-state (ISS) issues for damped wave equations with Dirichlet boundary conditions on a bounded domain of dimension two. The damping term is assumed to be non-linear and localized to an open subset of the domain. In a first step, we handle the undisturbed case as an extension of a previous work, where stability results are given with a damping term active on the full domain. Then, we address the case with disturbances and provide input-to-state types of results.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-03197202
Contributor : Meryem Kafnemer <>
Submitted on : Tuesday, April 13, 2021 - 3:59:23 PM
Last modification on : Friday, April 30, 2021 - 9:52:54 AM

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  • HAL Id : hal-03197202, version 1
  • ARXIV : 2005.06206

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Meryem Kafnemer, Benmiloud Mebkhout, Yacine Chitour. Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping. 2021. ⟨hal-03197202⟩

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