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

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics 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

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

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.