半线性热方程的爆破性质

Advances and Applications in Mathematical Sciences Pub Date : 2019-07-17 DOI:10.37516/adv.math.sci.2019.0080

Maan A. Rasheed

{"title":"半线性热方程的爆破性质","authors":"Maan A. Rasheed","doi":"10.37516/adv.math.sci.2019.0080","DOIUrl":null,"url":null,"abstract":"In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SOME BLOW-UP PROPERTIES OF A SEMILINEAR HEAT EQUATION\",\"authors\":\"Maan A. Rasheed\",\"doi\":\"10.37516/adv.math.sci.2019.0080\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.\",\"PeriodicalId\":53941,\"journal\":{\"name\":\"Advances and Applications in Mathematical Sciences\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances and Applications in Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37516/adv.math.sci.2019.0080\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances and Applications in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37516/adv.math.sci.2019.0080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑了一类非线性项为指数型的半线性热方程的爆破性质，该方程符合零dirichlet0边界条件，在𝑅𝑛中定义了一个球。首先，我们研究了爆炸集，表明爆炸只能发生在单点。其次，导出了上爆破率估计。

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

SOME BLOW-UP PROPERTIES OF A SEMILINEAR HEAT EQUATION

In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.

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

Advances and Applications in Mathematical Sciences MATHEMATICS-

CiteScore

0.50

自引率

0.00%

发文量