Global Existence and Blow-up of Solutions for a Class of Singular Parabolic Equations with Viscoelastic Term

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-28 DOI:10.1155/2024/5754129

Yanchao Gao, Wenxu Jia, Zhixin Feng

引用次数: 0

Abstract

In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.

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一类带粘弹性项的奇异抛物方程的全局存在性和膨胀解

本文考虑了一类带粘弹性项和对数项的奇异抛物方程的初始边界值问题。利用截断技术和 Faedo-Galerkin 近似方法，建立了弱解的局部存在性。基于势阱法，得出了弱解的全局存在性。此外，我们还利用凹性分析方法证明了弱解在有限时间内爆炸。

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.