具有对数非线性的伪抛物型$ p $-Kirchhoff方程的放大

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/eect.2023053

Hui Yang

{"title":"具有对数非线性的伪抛物型$ p $-Kirchhoff方程的放大","authors":"Hui Yang","doi":"10.3934/eect.2023053","DOIUrl":null,"url":null,"abstract":"In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Blow-up for a pseudo-parabolic $ p $-Kirchhoff equation with logarithmic nonlinearity\",\"authors\":\"Hui Yang\",\"doi\":\"10.3934/eect.2023053\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2023053\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/eect.2023053","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

研究了一类具有对数非线性的伪抛物型$ p $-Kirchhoff方程的初边值问题。通过证明该问题半流下不稳定集的不变性，采用Levine的凹性论证，建立了该问题的一般有限时间爆破判据，特别表明对于某些初始数据，该问题在任意高的初始能级上允许有限时间爆破解。此外，爆破解决方案的寿命是从上面估计的。

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

Blow-up for a pseudo-parabolic $ p $-Kirchhoff equation with logarithmic nonlinearity

In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.