{"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":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4003-4030"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400130","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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