AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Mathematics in Engineering Article
PDF (357.9 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions

Carmen Cortázar1, Fernando Quirós2,3( ), Noemí Wolanski4
Departamento de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049-Madrid, Spain
Instituto de Ciencias Matemáticas ICMAT (CSIC-UAM-UCM-UC3M), 28049-Madrid, Spain
IMAS-UBA-CONICET, Ciudad Universitaria, Pab. I, (1428) Buenos Aires, Argentina
Show Author Information

Abstract

We study the decay/growth rates in all L p norms of solutions to an inhomogeneous nonlocal heat equation in R N involving a Caputo α-time derivative and a power β of the Laplacian when the dimension is large, N > 4 β. Rates depend strongly on the space-time scale and on the time behavior of the spatial L 1 norm of the forcing term.

Keywords

heat equation with nonlocal time derivativeCaputo derivativefully nonlocal heat equationsfractional Laplacianlarge-time behavior

References

【1】
【1】
 
 
Crossref Google Scholar
Mathematics in Engineering
Volume 4 Issue 3,
June 2022
Pages 1-17
DOI: 10.3934/mine.2022022

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Cortázar C, Quirós F, Wolanski N. Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions. Mathematics in Engineering, 2022, 4(3): 1-17. https://doi.org/10.3934/mine.2022022

8

Views

1

Downloads

0

Crossref

0

Web of Science

1

Scopus
Received: 17 April 2021
Accepted: 07 July 2021
Published: 15 June 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)