Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing

Abstract EN

This paper deals with pullback dynamics for the weakly damped Schrödinger equation with time-dependent forcing.

An increasing, bounded, and pullback absorbing set is obtained if the forcing and its time-derivative are backward uniformly integrable.

Also, we obtain the forward absorption, which is only used to deduce the backward compact-decay decomposition according to high and low frequencies.

Based on a new existence theorem of a backward compact pullback attractor, we show that the nonautonomous Schrödinger equation has a pullback attractor which is compact in the past.

The method of energy, high-low frequency decomposition, Sobolev embedding, and interpolation are quite involved in calculating a priori pullback or forward bound.