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Journal Articles (Review Article) SIAM Journal on Control and Optimization Year : 2021

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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Dates and versions

hal-03197202 , version 1 (13-04-2021)

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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. SIAM Journal on Control and Optimization, 2021, ⟨10.1137/20M1337909⟩. ⟨hal-03197202⟩
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