Blow-Up and Global Existence of Solutions to Degenerate Kirchhoff Equation with Variable Source

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-29 DOI:10.1007/s00009-024-02677-2

Jingjing Zhang, Xiaolei Li

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.

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具有可变源的退化基尔霍夫方程的炸开和全局存在性解法

本文主要研究退化基尔霍夫（Kirchhoff）问题在不同条件下初能解的全局存在性和炸毁分类。首先，在亚临界或临界条件下，我们找到了两个不变集，并得到了有限时间内全局存在或炸毁的阈值结果。此外，我们应用 \(\omega \)极限证明了超临界初值能量情况下炸毁解的存在性。最后，我们给出了源项由扩散项控制时渐近行为的双面估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.