Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing
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 on...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/2139792 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566799711862784 |
|---|---|
| author | Lianbing She Yangrong Li Renhai Wang |
| author_facet | Lianbing She Yangrong Li Renhai Wang |
| author_sort | Lianbing She |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-10eddfe587054492b40662089df35a30 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-10eddfe587054492b40662089df35a302025-02-03T01:03:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/21397922139792Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent ForcingLianbing She0Yangrong Li1Renhai Wang2School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaThis 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.http://dx.doi.org/10.1155/2018/2139792 |
| spellingShingle | Lianbing She Yangrong Li Renhai Wang Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing Discrete Dynamics in Nature and Society |
| title | Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing |
| title_full | Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing |
| title_fullStr | Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing |
| title_full_unstemmed | Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing |
| title_short | Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing |
| title_sort | pullback forward dynamics for damped schrodinger equations with time dependent forcing |
| url | http://dx.doi.org/10.1155/2018/2139792 |
| work_keys_str_mv | AT lianbingshe pullbackforwarddynamicsfordampedschrodingerequationswithtimedependentforcing AT yangrongli pullbackforwarddynamicsfordampedschrodingerequationswithtimedependentforcing AT renhaiwang pullbackforwarddynamicsfordampedschrodingerequationswithtimedependentforcing |