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

Lianbing She, Yangrong Li and Renhai Wang

Discrete Dynamics in Nature and Society, 2018, vol. 2018, 1-14

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:2139792

DOI: 10.1155/2018/2139792

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