Stability analysis of a 1D wave equation with a nonmonotone distributed damping. Issue 16 (2019)

• Record Type: Journal Article
• Authors: Marx, Swann; Chitour, Yacine; Prieur, Christophe
• Is Part Of: IFAC-PapersOnLine. Volume 52:Issue 16(2019)
• Page Start: 36
• Page End: 41
• Publication Date: 2019
• Subjects: 1D wave equation -- nonlinear control -- Lyapunov functionals; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2019.11.752
• Languages: English
• ISSNs: 2405-8963

Abstract

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.