Stability Analysis of a 1D Wave Equation with a Nonmonotone Distributed Damping

Swann Marx1, Yacine Chitour2, Christophe Prieur3

  • 1LAAS-CNRS
  • 2Universit\'e Paris-Sud, CNRS, centralesupelec
  • 3CNRS

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Invited Session

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10:00 - 12:00 | Wed 4 Sep | Room FH 2 | WeB2

Control of Nonlinear PDEs I

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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 $pin [2,infty]$, and relies mostly on some results collected in cite{haraux1D}. The asymptotic behavior analysis is based on an attractivity result on a specific infinite-dimensional linear time-variant system.

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