INVARIANT-MANIFOLDS FOR RETARDED SEMILINEAR WAVE-EQUATIONS

By means of a nonlinear variation of constants formula it is shown tha t, under suitable assumptions, there exists a global invariant manifol d for semilinear hyperbolic evolution equations with a retarded pertur bation, provided that the time-delay is small or the magnitude and the Lipschitz constant of the perturbation are small. By construction, th is invariant manifold is weaved by trajectories of an associated nonre tarded evolution equation; it is also locally exponentially attracting . As applications of the theory, we treat retarded perturbutions of th e Sine-Gordon equation and the dissipative Klein-Gordon equation. (C) 1994 Academic Press, Inc.