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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
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Submitted on : Tuesday, February 5, 2019 - 10:43:14 AM
Last modification on : Monday, July 4, 2022 - 9:36:59 AM
Long-term archiving on: : Monday, May 6, 2019 - 1:41:13 PM

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Swann Marx, yacine Chitour, Christophe Prieur. Stability analysis of a 1D wave equation with a nonmonotone distributed damping. MECHATRONICS 2019 - NOLCOS 2019 - 8th IFAC Symposium on Mechatronic Systems - 11th IFAC Symposium on Nonlinear Control Systems, Sep 2019, Vienne, Austria. ⟨10.1016/j.ifacol.2019.11.752⟩. ⟨hal-02006292⟩

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