Pullback attractors for the nonclassical diffusion equations with memory in time-dependent spaces

被引：1

作者：

Li, Ke ^{[1
]}

Xie, Yongqin ^{[1
,2
]}

Ren, Yong ^{[2
]}

Li, Jun ^{[1
]}

机构：

[1] Hunan Univ Informat Technol, Sch Gen Educ, Changsha 410151, Hunan, Peoples R China

[2] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

基金：

中国国家自然科学基金;

关键词：

nonclassical diffusion equation; time-dependent global attractor; memory; unbounded domain; ASYMPTOTIC-BEHAVIOR; HEAT-CONDUCTION; WAVE-EQUATIONS; DYNAMICS;

D O I：

10.3934/math.20231561

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the asymptotic behavior of nonclassical diffusion equations with hereditary memory and time-dependent perturbed parameter on whole space Rn. Under a general assumption on the memory kernel k, the existence and regularity of time-dependent global attractors are proven using a new analytical technique. It is remarkable that the nonlinearity f has no restriction on the upper growth.

引用

页码：30537 / 30561

页数：25

共 46 条

[1] ON THE PROBLEM OF DIFFUSION IN SOLIDS [J].

AIFANTIS, EC .

ACTA MECHANICA, 1980, 37 (3-4) :265-296

[2] Strong Solutions of the Incompressible Navier-Stokes-Voigt Model [J].

Baranovskii, Evgenii S. .

MATHEMATICS, 2020, 8 (02)

[3]

Barenblatt G.E., 1960, J APPL MATH USSR, V24, P12861303, DOI DOI 10.1016/0021-8928(60)90107-6

[4]

Carvalho A.N., 2013, Attractors for Infinite-Dimensional Non- autonomous Dynamical Systems, V182, DOI [10.1007/978-1-4614-4581-4, DOI 10.1007/978-1-4614-4581-4]

[5] ON A THEORY OF HEAT CONDUCTION INVOLVING 2 TEMPERATURES [J].

CHEN, PJ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1968, 19 (04) :614-&

[6] On trajectory and global attractors for semilinear heat equations with fading memory [J].

Chepyzhov, VV ;

Miranville, A .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (01) :119-167

[7] NONCLASSICAL DIFFUSION WITH MEMORY LACKING INSTANTANEOUS DAMPING [J].

Conti, Monica ;

Dell'Oro, Filippo ;

Pata, Vittorino .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (04) :2035-2050

[8] A Remark on Nonclassical Diffusion Equations with Memory [J].

Conti, Monica ;

Marchini, Elsa M. .

APPLIED MATHEMATICS AND OPTIMIZATION, 2016, 73 (01) :1-21

[9] Nonclassical diffusion with memory [J].

Conti, Monica ;

Marchini, Elsa M. ;

Pata, Vittorino .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (05) :948-958

[10] Asymptotic structure of the attractor for processes on time-dependent spaces [J].

Conti, Monica ;

Pata, Vittorino .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 19 :1-10

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