Dynamics for the damped Boussinesq equation with delay

This paper is concerned with the dynamical behavior of the damped Boussinesq equation containing a delay forcing term. It shows that, under suitable dissipative conditions, such a system possesses a pullback attractor and a uniform forward attractor in [Formula: see text].

PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS

The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay forcing term which, in particular, covers the models of sine–Gordon type. The result follows from the existence of a compact set which is uniformly attracting for the two-parameter semigroup associated to the model.