完全非局部扩散方程的熵解

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-09-01 DOI:10.1002/mana.202400130

Ying Li, Chao Zhang

{"title":"完全非局部扩散方程的熵解","authors":"Ying Li, Chao Zhang","doi":"10.1002/mana.202400130","DOIUrl":null,"url":null,"abstract":"We consider the fully nonlocal diffusion equations with nonnegative <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.","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":"{\"title\":\"Entropy solutions to the fully nonlocal diffusion equations\",\"authors\":\"Ying Li, Chao Zhang\",\"doi\":\"10.1002/mana.202400130\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the fully nonlocal diffusion equations with nonnegative <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.\",\"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}","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

摘要

我们考虑了具有非负数据的完全非局部扩散方程。基于近似和能量方法，我们证明了此类问题的非负熵解的存在性和唯一性。我们的结果尤其适用于时空分数拉普拉斯方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Entropy solutions to the fully nonlocal diffusion equations

We consider the fully nonlocal diffusion equations with nonnegative $L^{1}$ -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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

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