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

Fuente: arXiv
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Main Authors: Xu, Jiaohui, Caraballo, Tomás, Valero, José
Format: Preprint
Published: 2024
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author Xu, Jiaohui
Caraballo, Tomás
Valero, José
author_facet Xu, Jiaohui
Caraballo, Tomás
Valero, José
contents In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is different from 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_17923
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion
Xu, Jiaohui
Caraballo, Tomás
Valero, José
Analysis of PDEs
Dynamical Systems
35B40, 35K05, 37L30, 45K05
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is different from 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.
title Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion
topic Analysis of PDEs
Dynamical Systems
35B40, 35K05, 37L30, 45K05
url https://arxiv.org/abs/2407.17923