Uniform Attractor and Approximate Inertial Manifolds for Nonautonomous Long-Short Wave Equations

Abstract

Nonautonomous long-short wave equations with quasiperiodic forces are studied. We prove the existence of the uniform attractor for the system by means of energy method, which is widely used to deal with problems who have no continuity (with respect to the initial data) property, as well as to those which Sobolev compact imbedding cannot be applied. Afterwards, we construct an approximate inertial manifold by means of extending phase space method and we estimated the size of the corresponding attracting neighborhood for this manifold.