P. Pucci et J. Serrin, ASYMPTOTIC STABILITY FOR NONAUTONOMOUS DISSIPATIVE WAVE SYSTEMS, Communications on pure and applied mathematics, 49(2), 1996, pp. 177-216
We study the problem of asymptotic stability, as time tends to infinit
y, of solutions of dissipative wave systems, governed by time-dependen
t nonlinear damping forces and subject to the action of strongly nonli
near potential energies. In the final part of the paper we also consid
er the case of polyharmonic wave operators and higher-order dissipatio
n terms. (C) 1996 John Wiley & Sons, Inc.