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Conference Papers Year : 2019

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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Dates and versions

hal-02006292 , version 1 (05-02-2019)

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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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