On some fractional parabolic reaction-diffusion systems with gradient source terms

IF 2.5 2区 数学 Q1 MATHEMATICS
Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri
{"title":"On some fractional parabolic reaction-diffusion systems with gradient source terms","authors":"Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri","doi":"10.1007/s13540-024-00316-x","DOIUrl":null,"url":null,"abstract":"<p>The present paper is concerned with a fractional parabolic reaction-diffusion system posed in a regular bounded open subset of <span>\\({\\mathbb {R}}^N\\)</span>, where the gradients of the unknowns act as source terms (see (<i>S</i>) below). First, we establish some nonexistence and blow-up in finite time results. Second, we prove some new weighted regularity results. Such results are interesting in themselves and play a crucial role to study local existence of nonnegative solutions to our system under suitable assumptions on the data. This work also highlights a substantial difference between the nonlocal case and the local case already studied by the fourth author and his coworkers.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"4 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00316-x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

The present paper is concerned with a fractional parabolic reaction-diffusion system posed in a regular bounded open subset of \({\mathbb {R}}^N\), where the gradients of the unknowns act as source terms (see (S) below). First, we establish some nonexistence and blow-up in finite time results. Second, we prove some new weighted regularity results. Such results are interesting in themselves and play a crucial role to study local existence of nonnegative solutions to our system under suitable assumptions on the data. This work also highlights a substantial difference between the nonlocal case and the local case already studied by the fourth author and his coworkers.

Abstract Image

关于一些带有梯度源项的分数抛物线反应扩散系统
本文关注的是在\({\mathbb {R}}^N\) 的规则有界开放子集中提出的分数抛物面反应扩散系统,其中未知数的梯度作为源项(见下文 (S))。首先,我们建立了一些不存在和在有限时间内炸毁的结果。其次,我们证明了一些新的加权正则性结果。这些结果本身就很有趣,而且对研究我们系统在适当数据假设下非负解的局部存在性起着至关重要的作用。这项工作还凸显了非局部情况与第四作者及其同事已经研究过的局部情况之间的本质区别。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Fractional Calculus and Applied Analysis
Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
4.70
自引率
16.70%
发文量
101
期刊介绍: Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信