{"title":"Upper bounds for the blow-up time of the 2-d parabolic-elliptic Patlak-Keller-Segel model of chemotaxis","authors":"Patrick Maheux","doi":"10.1016/j.jmaa.2025.129487","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we obtain upper bounds for the critical time <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the total mass is assumed. The result is expressed not only in terms of supercritical mass <span><math><mi>M</mi><mo>></mo><mn>8</mn><mi>π</mi></math></span>, but also in terms of the <em>shape</em> of the initial data.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129487"},"PeriodicalIF":1.2000,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25002689","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we obtain upper bounds for the critical time of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the total mass is assumed. The result is expressed not only in terms of supercritical mass , but also in terms of the shape of the initial data.
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The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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