分层李群上的Fujita指数

IF 0.7 2区 数学 Q2 MATHEMATICS
Durvudkhan Suragan, Bharat Talwar
{"title":"分层李群上的Fujita指数","authors":"Durvudkhan Suragan, Bharat Talwar","doi":"10.1007/s13348-023-00427-3","DOIUrl":null,"url":null,"abstract":"<p>We prove that <span>\\(\\frac{Q}{Q-2}\\)</span> is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension <i>Q</i>. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon the group elements and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fujita exponent on stratified Lie groups\",\"authors\":\"Durvudkhan Suragan, Bharat Talwar\",\"doi\":\"10.1007/s13348-023-00427-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that <span>\\\\(\\\\frac{Q}{Q-2}\\\\)</span> is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension <i>Q</i>. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon the group elements and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.</p>\",\"PeriodicalId\":50993,\"journal\":{\"name\":\"Collectanea Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Collectanea Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13348-023-00427-3\",\"RegionNum\":2,\"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":"Collectanea Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13348-023-00427-3","RegionNum":2,"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

我们证明了在任意齐次维数q的分层李群上的半线性热方程\(\frac{Q}{Q-2}\)是Fujita指数,这涵盖了欧几里德情形,并对幂零李群的证明技术有了新的认识。我们研究的方程有一个强迫项,它只依赖于群元素,并且具有正积分。分层李群结构与测试函数法、Banach不动点定理在证明中起着重要的作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fujita exponent on stratified Lie groups

We prove that \(\frac{Q}{Q-2}\) is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension Q. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon the group elements and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.

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
Collectanea Mathematica
Collectanea Mathematica 数学-数学
CiteScore
2.70
自引率
9.10%
发文量
36
审稿时长
>12 weeks
期刊介绍: Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信