IMPLICATIONS OF SHARP TRACE REGULARITY RESULTS ON BOUNDARY STABILIZATION OF THE SYSTEM OF LINEAR ELASTICITY

Uniform exponential decay of solution is established for the elastodyn amic system of elasticity using boundary feedback control. Energy diss ipation is introduced via linear velocity feedbacks acting through a p ortion of the boundary as traction forces. Two primary goals are achie ved: First, these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary, thus extending earlier work which required that the domain be ''star shaped .'' Second, the feedback is only a function of velocity, as opposed to also containing the tangential derivative of the displacement, result ing in a physically viable feedback. Proof is based on the multiplier method and relies critically on sharp trace estimates for the tangenti al derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system. (C) 1998 Ac ademic Press.