一类分数阶演化方程严格解的存在性和正则性

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-10-22 DOI:10.1002/mana.202400074

Guang Meng Wu, Jia Wei He

{"title":"一类分数阶演化方程严格解的存在性和正则性","authors":"Guang Meng Wu, Jia Wei He","doi":"10.1002/mana.202400074","DOIUrl":null,"url":null,"abstract":"We study the existence and Hölder regularity of solutions for fractional evolution equations of order <math>\n <semantics>\n <mrow>\n <mi>α</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mn>2</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$\\alpha \\in (1,2)$</annotation>\n </semantics></math>. By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4730-4749"},"PeriodicalIF":0.8000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and regularity of strict solutions for a class of fractional evolution equations\",\"authors\":\"Guang Meng Wu, Jia Wei He\",\"doi\":\"10.1002/mana.202400074\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the existence and Hölder regularity of solutions for fractional evolution equations of order <math>\\n <semantics>\\n <mrow>\\n <mi>α</mi>\\n <mo>∈</mo>\\n <mo>(</mo>\\n <mn>1</mn>\\n <mo>,</mo>\\n <mn>2</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\alpha \\\\in (1,2)$</annotation>\\n </semantics></math>. By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"297 12\",\"pages\":\"4730-4749\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-10-22\",\"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.202400074\",\"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.202400074","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

研究了α∈(1,2)$ \alpha \in(1,2)$阶分数阶演化方程解的存在性和Hölder正则性。利用解析解构造插值空间，有效地降低了初始数据的正则性。利用插值空间和解析解的一些性质，导出了一类非齐次问题严格解的存在性和Hölder正则性，以及一类非线性问题严格解的存在性和Hölder正则性。

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

Existence and regularity of strict solutions for a class of fractional evolution equations

We study the existence and Hölder regularity of solutions for fractional evolution equations of order $α \in (1, 2)$ . By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.

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