Invariant Manifolds for Retarded Semilinear Wave Equations

Abstract

Listen

Translate article

By means of a nonlinear variation of constants formula it is shown that, under suitable assumptions, there exists a global invariant manifold for semilinear hyperbolic evolution equations with a retarded perturbation, provided that the time-delay is small or the magnitude and the Lipschitz constant of the perturbation are small. By construction, this invariant manifold is weaved by trajectories of an associated nonretarded evolution equation; it is also locally exponentially attracting. As applications of the theory, we treat retarded perturbutions of the Sine-Gordon equation and the dissipative Klein-Gordon equation.