Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

被引：0
作者：
Dong, Xiaolei [1 ]
Qin, Yuming [2 ,3 ]
机构：
[1] Donghua Univ, Coll Informat Sci & Technol, Shanghai 201620, Peoples R China
[2] Donghua Univ, Dept Math, Shanghai 201620, Peoples R China
[3] Donghua Univ, Inst Nonlinear Sci, Shanghai 201620, Peoples R China
来源：
AIMS MATHEMATICS | 2022年 / 7卷 / 05期
基金：
中国国家自然科学基金;
关键词：
nonclassical di ffusion equations; finite fractal dimension; pullback attractors; GLOBAL ATTRACTORS; UPPER SEMICONTINUITY; ASYMPTOTIC-BEHAVIOR; UNIFORM ATTRACTORS; EXISTENCE; DYNAMICS;
D O I：
10.3934/math.2022449
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical di ffusion equation in H-0(1) (Omega). First, we prove the existence of pullback attractors for a nonclassical di ffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by [6], we prove the finite fractal dimension of pullback attractors for a nonclassical di ffusion equation in H-0(1) (Omega)..
引用
收藏
页码：8064 / 8079
页数：16
相关论文
共 53 条
[31]   Attractors for the semilinear reaction-diffusion equation with distribution derivatives in unbounded domains [J].
Sun, CY ;
Zhong, CK .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (01) :49-65
[32]   Attractors for reaction-diffusion equations in unbounded domains [J].
Wang, BX .
PHYSICA D-NONLINEAR PHENOMENA, 1999, 128 (01) :41-52
[33]   Bi-spatial Pullback Attractors of Fractional Nonclassical Diffusion Equations on Unbounded Domains with (p, q)-Growth Nonlinearities [J].
Wang, Renhai ;
Li, Yangrong ;
Wang, Bixiang .
APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 84 (01) :425-461
[34]   Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on RN [J].
Wang, Renhai ;
Shi, Lin ;
Wang, Bixiang .
NONLINEARITY, 2019, 32 (11) :4524-4556
[35]   RANDOM DYNAMICS OF FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS DRIVEN BY COLORED NOISE [J].
Wang, Renhai ;
Li, Yangrong ;
Wang, Bixiang .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (07) :4091-4126
[36]   On the dynamics of a class of nonclassical parabolic equations [J].
Wang, SY ;
Li, DS ;
Zhong, CK .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (02) :565-582
[37]   Attractors for the nonclassical diffusion equations with fading memory [J].
Wang, Xuan ;
Yang, Lu ;
Zhong, Chengkui .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 362 (02) :327-337
[38]   Attractors for the non-autonomous nonclassical diffusion equations with fading memory [J].
Wang, Xuan ;
Zhong, Chengkui .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (11) :5733-5746
[39]   On the existence of pullback attractors for non-autonomous reaction-diffusion equations [J].
Wang, Yonghai ;
Zhong, Chengkui .
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2008, 23 (01) :1-16
[40]   Regularity of pullback attractors for nonautonomous nonclassical diffusion equations [J].
Wang, Yonghai ;
Zhu, Zilong ;
Li, Pengrui .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 459 (01) :16-31
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