  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
$\in$ [2, $\infty$], 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.
