[1]佘连兵,张文林,李扬荣.非自治Reaction-Diffusion方程的后向紧吸引子的正则性[J].四川师范大学学报(自然科学版),2020,43(04):492-497.[doi:10.3969/j.issn.1001-8395.2020.04.012]
 SHE Lianbing,ZHANG Wenlin,LI Yangrong.Regularity of Backward Compact Pullback Attractors for Non-autonomous Reaction-Diffusion Equations[J].Journal of SichuanNormal University,2020,43(04):492-497.[doi:10.3969/j.issn.1001-8395.2020.04.012]
点击复制

非自治Reaction-Diffusion方程的后向紧吸引子的正则性()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年04期
页码:
492-497
栏目:
基础理论
出版日期:
2020-06-20

文章信息/Info

Title:
Regularity of Backward Compact Pullback Attractors for Non-autonomous Reaction-Diffusion Equations
文章编号:
1001-8395(2020)04-0492-06
作者:
佘连兵1 张文林1 李扬荣2
1. 六盘水师范学院 数学与信息工程学院, 贵州 六盘水 553004; 2. 西南大学 数学与统计学院, 重庆 400715
Author(s):
SHE Lianbing1 ZHANG Wenlin1 LI Yangrong2
1. School of Mathematics and Information Engineering, Liupanshui Normal University, Liupanshui 553004, Guizhou; 2. School of Mathematics and Statistics, Southwest University, Chongqing 400715
关键词:
非自治Reaction-Diffusion方程 拉回吸引子 后向紧性 正则性
Keywords:
non-autonomous Reaction-Diffusion equation pullback attractor backward compactness regularity
分类号:
O193
DOI:
10.3969/j.issn.1001-8395.2020.04.012
文献标志码:
A
摘要:
运用后向Gronwall型不等式及一个后向截断的方法,在g是后向绝对连续的假设条件下,证明非自治Reaction-Diffusion方程在正则p(p≥2)次可积空间上存在唯一的后向紧拉回吸引子,这种紧性体现了非自治系统关于时间依赖的独特性,展示了非自治系统和自治系统的本质区别.
Abstract:
Combing a backward Gronwall-type inequality and a truncation technique, we show that the non-autonomous Reaction-Diffusion equation has a unique backward compact pullback attractor in me integrable spaces when the time-dependent force is backward absolutely continuous. This backward compactness of the attractor reflects the time-dependent feature of the non-autonomous dynamical system, and reveals the essential distinction between non-autonomous systems and autonomous systems.

参考文献/References:

[1] CARABALLO T, CARABALLO A N, LANGA J A, et al. Existence of pullback attractors for pullback asymptotically compact processes[J]. Nonlinear Analysis:TMA,2010,72(3/4):1967-1976.
[2] WANG B X. Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems[J]. J Differential Equations,2012,253(5):1544-1583.
[3] LI Y R, GU A H, LI J. Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations[J]. J Differential Equations,2015,258(2):504-534.
[4] LI Y R, YIN J Y. A modified proof of pullback attractors in a Sobolev space for stochastic FitzHugh-Nagumo equations[J]. Discrete and Continuous Dynamical Systems,2016,21(4):1203-1223.
[5] CARABALLO A, LANGA J A, ROBINSON J C. Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems[M]. New York:Springer-Verlag,2013.
[6] LI Y R, WANG R H, YIN J Y. Bankward compact attrators for non-autonomous Benjsmin-Bona-Mahony equations on unbounded channels[J]. Discrete and Continuous Dynamical Systems,2017,22(7):2569-2586.
[7] YIN J Y, GU A H, LI Y R. Bankwards compact attrators for non-autonomous damped 3D Navier-Stoks equations[J]. Dynamics PDE,2017,14(2):201-218.
[8] YIN J Y, LI Y R, GU A H. Backwards compact attractors and periodic attractors for non-autonomous damped wave equations on an unbounded domain[J]. Computers & Mathematics with Applications,2017,74(4):744-758.
[9] SHE L B, LI Y R, WANG R H. Pullback-forward dynamics for damped Schrödinger equations with time-dependent forcing[J]. Discrete Dynamics in Nature and Society,2018,2018(3):1-14.
[10] 佘连兵,王仁海. 非自治Reaction-Diffusion方程后项紧的拉回吸引子的存在性[J]. 四川师范大学学报(自然科学版),2017,40(6):1-5.
[11] 佘连兵,李信韬,李扬荣. 无界域上非自治Reaction-Diffusion方程的后向紧动力学[J]. 西南大学学报(自然科学版),2018,40(9):59-66.
[12] SONG H T. Pullback attractors of non-autonomous Reaction-Diffusion equations in H10[J]. J Differential Equations,2009,249(10):2357-2376.

相似文献/References:

[1]赵克发,马巧珍*.非自治反应扩散方程拉回吸引子的存在性[J].四川师范大学学报(自然科学版),2015,(02):182.[doi:10.3969/j.issn.1001-8395.2015.02.006]
 ZHAO Kefa,MA Qiaozhen.The Existence of Pullback Attractors for Non-autonomous Reaction-Diffusion Equations[J].Journal of SichuanNormal University,2015,(04):182.[doi:10.3969/j.issn.1001-8395.2015.02.006]
[2]佘连兵,王仁海.非自治反映扩散方程后项紧拉回吸引子的存在性[J].四川师范大学学报(自然科学版),2017,(06):797.[doi:10.3969/j.issn.1001-8395.2017.06.015]
 SHE Lianbing,WANG Renhai.The Backward Compactness of Pullback Attractors for Nonautonomous Reaction-Diffusion Equations[J].Journal of SichuanNormal University,2017,(04):797.[doi:10.3969/j.issn.1001-8395.2017.06.015]
[3]文慧霞,舒 级*,李林芳.一类非自治随机波动方程的随机吸引子[J].四川师范大学学报(自然科学版),2019,42(02):168.[doi:10.3969/j.issn.1001-8395.2019.02.004]
 WEN Huixia,SHU Ji,LI Linfang.The Random Attractors of a Class of Non-autonomous Stochastic Wave Equations[J].Journal of SichuanNormal University,2019,42(04):168.[doi:10.3969/j.issn.1001-8395.2019.02.004]
[4]胡华书,蒲志林*,沈怡心.一类带有扩散项和阶段结构的非自治捕食-食饵系统解的渐近行为[J].四川师范大学学报(自然科学版),2019,42(04):443.[doi:10.3969/j.issn.1001-8395.2019.04.002]
 HU Huashu,PU Zhilin,SHEN Yixin.prey Systems with Diffusion and Stage Structure[J].Journal of SichuanNormal University,2019,42(04):443.[doi:10.3969/j.issn.1001-8395.2019.04.002]

备注/Memo

备注/Memo:
收稿日期:2019-01-12 接受日期:2019-04-16
基金项目:国家自然科学基金(11571283)、贵州省教育厅自然科学基金(KY[2019]139、[2019]143)和贵州省科学技术基金(黔科合基础[2020]1Y007)
第一作者简介:佘连兵(1981—),男,副教授,主要从事无穷维动力系统的研究,E-mail:shelianbing@163.com
更新日期/Last Update: 2020-06-20