河北师范大学学报(自然科学版)2025,Vol.49Issue(1) :25-32.DOI:10.13763/j.cnki.jhebnu.nse.202501001

非局部时滞抛物方程渐近性态的研究

Asymptotic Behavior of Parabolic Equations with Time Non-local Delay

李心 殷美娟
河北师范大学学报(自然科学版)2025,Vol.49Issue(1) :25-32.DOI:10.13763/j.cnki.jhebnu.nse.202501001

非局部时滞抛物方程渐近性态的研究

Asymptotic Behavior of Parabolic Equations with Time Non-local Delay

李心 1殷美娟1
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作者信息

  • 1. 燕山大学理学院,秦皇岛 066004
  • 折叠

摘要

文章主要研究全空间上非局部时滞抛物方程在Dirichlet边界条件下的渐近性态问题.利用先验估计得到拉回吸收集的存在,通过选取一类新型截断函数,结合尾项估计的方法,克服了非局部性全空间问题特有的紧性验证困难,得到了时滞分数阶反应扩散方程解的渐近紧性,进而得到全空间中拉回吸引子的存在.

Abstract

This paper deals with the asymptotic behavior of parabolic equations with non-local delay in whole space under Dirichlet boundary conditions.The existence of the pullback absorption set is obtained by a priori estimation.By selecting a new type of truncation function and combining it with the method of tail term estimation,the difficulty of compactness verification is overcome,and the asymptotic compactness of the solution of the fractional reaction-diffusion equation with delay is obtained,and the existence of the pullback attractor in the whole space is also obtained.

关键词

分数阶算子/时滞/反应扩散方程/拉回吸引子

Key words

fractional operator/time delay/reaction diffusion equation/pullback attractors

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出版年

2025
河北师范大学学报(自然科学版)
河北师范大学

河北师范大学学报(自然科学版)

影响因子:0.291
ISSN:1000-5854
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