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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri
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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。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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