Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces

被引：0

作者：

Shi, Yadan ^{[1
]}

Xie, Yongqin ^{[1
,2
]}

Li, Ke ^{[1
]}

Tang, Zhipiao ^{[1
]}

机构：

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

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

来源：

ELECTRONIC RESEARCH ARCHIVE | 2024年 / 32卷 / 12期

关键词：

nonclassical diffusion equation; pullback attractors; nonlinear delay; polynomial growth; ASYMPTOTIC-BEHAVIOR; HEAT-CONDUCTION; WAVE-EQUATIONS;

D O I：

10.3934/era.2024320

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, we primarily investigate the asymptotic behavior of solutions associated with a nonclassical diffusion process by memory effects and a perturbed parameter that varies over time. A significant innovation is the consideration of a delay term governed by a function with minimal assumptions: merely measurability and a phase-space that is a time-dependent space of continuouslytime-varying functions. By employing a novel analytical approach, we demonstrate the existence and regularity of time-varying pullback D-attractors. Notably, the nonlinearity f is unrestricted by any upper limit on its growth rate.

引用

页码：6847 / 6868

页数：22

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