{"title":"Blow-Up and Global Existence of Solutions to Degenerate Kirchhoff Equation with Variable Source","authors":"Jingjing Zhang, Xiaolei Li","doi":"10.1007/s00009-024-02677-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we mainly study the classification of global existence and blow-up of solutions to degenerate Kirchhoff problems for the initial energy at different conditions. Firstly, under subcritical or critical conditions, we find two invariant sets and obtain the threshold results of global existence or blow-up in finite time. Furthermore, we apply <span>\\(\\omega \\)</span>-limit to prove the existence of blow-up solutions for the supercritical initial energy case. Finally, we give two-sided estimates of asymptotic behavior when the source term is controlled by the diffusion term.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mediterranean Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02677-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we mainly study the classification of global existence and blow-up of solutions to degenerate Kirchhoff problems for the initial energy at different conditions. Firstly, under subcritical or critical conditions, we find two invariant sets and obtain the threshold results of global existence or blow-up in finite time. Furthermore, we apply \(\omega \)-limit to prove the existence of blow-up solutions for the supercritical initial energy case. Finally, we give two-sided estimates of asymptotic behavior when the source term is controlled by the diffusion term.
期刊介绍：
The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003.
The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience.
In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.
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