Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing
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A Priori
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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.
2013 ◽
Vol 12
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pp. 1340001
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2021 ◽
Vol 7
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2005 ◽
Vol 50
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pp. 1345-1362
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1993 ◽
Vol 99
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pp. 4590-4596
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1979 ◽
Vol 43
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pp. 512-515
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2010 ◽
Vol 138
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pp. 4359-4359
2014 ◽
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pp. A1-A19
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1999 ◽
Vol 40
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pp. 3268-3274
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