Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion

被引：22

作者：

Xu, Jiaohui ^{[1
]}

Caraballo, Tomas ^{[1
]}

Valero, Jose ^{[2
]}

机构：

[1] Univ Seville, Fac Matemat, Dept Ecuac Diferenciales & Anal Numer, C-Tarfia s-n, 41012 Seville, Spain

[2] Avda Univ, Univ Miguel Hernandez, Ctr Invest Operat, s-n, 03202 Elche, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 327卷

关键词：

Non-local partial differential equations; Long time memory; Dafermos transformation; Global attractors; ATTRACTORS; EQUATIONS;

D O I：

10.1016/j.jde.2022.04.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and nonlocal diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is different from ones used in the previous published literature on the long time behavior of heat equations with memory, which is carried out by the Dafermos transformation. As a consequence, the obtained results provide complete information about the attracting sets for the original problem, instead of the transformed one. In particular, the proved results also generalize and complete previous literature in the local case. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：418 / 447

页数：30

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