GALERKIN STABILITY OF PULLBACK ATTRACTORS FOR NONAUTONOMOUS NONLOCAL EQUATIONS

被引：2

作者：

Wang, Shulin ^{[1
]}

Li, Yangrong ^{[2
]}

机构：

[1] Southwest Univ, Fac Educt, Chongqing 400715, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 10期

关键词：

Nonlocal equation; pullback attractor; Galerkin approximation; back-ward compactness; upper semicontinuity; PARTIAL-DIFFERENTIAL-EQUATIONS; EXISTENCE; BEHAVIOR;

D O I：

10.3934/dcdss.2023027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. We show that the nth Galerkin approximation system has a pullback attractor in the n-dimensional subspace of the Lebesgue space. We then prove that the sequence of Galerkin pullback attractors is uniformly backward bounded and that the sequence of Galerkin solutions converges uniformly on any bounded set. Using these results, we es-tablish upper semi-convergence of the sequence of Galerkin pullback attractors towards the pullback attractors of the original infinite-dimensional system.

引用

页码：2800 / 2814

页数：15

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