WEAK ASYMPTOTIC STABILITY OF 2ND-ORDER EVOLUTION-EQUATIONS BY NONLINEAR AND NONMONOTONE FEEDBACKS

We consider the problem of asymptotic decay as t --> +infinity solutio ns of an abstract evolution equation of second order with a nonlinear and nonmonotone feedback. Weak asymptotic stability of the global solu tions is proved. This abstract result can be applied to different type s of equations (wave, beam, and plate equations) and to different type s of controls (interior, boundary, or pointwise controls). In particul ar, we significantly improve several earlier results on the asymptotic stability of the wave equation in a bounded domain with an interior o r boundary control.