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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00316-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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.