Franka Baaske, Hans-Jürgen Schmeißer, Hans Triebel
{"title":"分数非线性热方程和以分数高斯-韦尔斯特拉斯半群表示的某些函数空间的特征","authors":"Franka Baaske, Hans-Jürgen Schmeißer, Hans Triebel","doi":"10.1007/s13163-024-00488-3","DOIUrl":null,"url":null,"abstract":"<p>We present a new proof of the caloric smoothing related to the fractional Gauss–Weierstrass semi–group in Triebel-Lizorkin spaces. This property will be used to prove existence and uniqueness of mild and strong solutions of the Cauchy problem for a fractional nonlinear heat equation.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional nonlinear heat equations and characterizations of some function spaces in terms of fractional Gauss–Weierstrass semi–groups\",\"authors\":\"Franka Baaske, Hans-Jürgen Schmeißer, Hans Triebel\",\"doi\":\"10.1007/s13163-024-00488-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present a new proof of the caloric smoothing related to the fractional Gauss–Weierstrass semi–group in Triebel-Lizorkin spaces. This property will be used to prove existence and uniqueness of mild and strong solutions of the Cauchy problem for a fractional nonlinear heat equation.</p>\",\"PeriodicalId\":501429,\"journal\":{\"name\":\"Revista Matemática Complutense\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matemática Complutense\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13163-024-00488-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matemática Complutense","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13163-024-00488-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fractional nonlinear heat equations and characterizations of some function spaces in terms of fractional Gauss–Weierstrass semi–groups
We present a new proof of the caloric smoothing related to the fractional Gauss–Weierstrass semi–group in Triebel-Lizorkin spaces. This property will be used to prove existence and uniqueness of mild and strong solutions of the Cauchy problem for a fractional nonlinear heat equation.
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