{"title":"Entropy solutions to the fully nonlocal diffusion equations","authors":"Ying Li, Chao Zhang","doi":"10.1002/mana.202400130","DOIUrl":null,"url":null,"abstract":"<p>We consider the fully nonlocal diffusion equations with nonnegative <span></span><math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mn>1</mn>\n </msup>\n <annotation>$L^1$</annotation>\n </semantics></math>-data. Based on the approximation and energy methods, we prove the existence and uniqueness of nonnegative entropy solutions for such problems. In particular, our results are valid for the time-space fractional Laplacian equations.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400130","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the fully nonlocal diffusion equations with nonnegative -data. Based on the approximation and energy methods, we prove the existence and uniqueness of nonnegative entropy solutions for such problems. In particular, our results are valid for the time-space fractional Laplacian equations.
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