Stabilizability of Systems of One-Dimensional Wave Equations by One Internal or Boundary Control Force

Abstract

We study the internal and boundary stabilizability of a system of wave equations by one control force. We prove that the "classical" internal damping applied to only one of the equations never gives exponential stability if the wave speeds are different and, if the wave speeds are the same, we give explicit necessary and sufficient conditions for the stability to occur. We also study the simultaneous boundary stabilization of the same system.