Stability analysis of a 1D wave equation with a nonmonotone distributed damping

Abstract : This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic behavior of the trajectories of the system under consideration. The well-posedness is proved in the nonstandard L p functional spaces, with p ∈ [2, ∞], and relies mostly on some results collected in Haraux (2009). The asymptotic behavior analysis is based on an attractivity result on a specific infinite-dimensional linear time-variant system.
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https://hal.laas.fr/hal-02006292
Contributor : Swann Marx <>
Submitted on : Tuesday, February 5, 2019 - 10:43:14 AM
Last modification on : Tuesday, April 9, 2019 - 4:12:02 PM
Long-term archiving on : Monday, May 6, 2019 - 1:41:13 PM

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  • HAL Id : hal-02006292, version 1
  • ARXIV : 1902.02050

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Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of a 1D wave equation with a nonmonotone distributed damping. 2019. ⟨hal-02006292⟩

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