一类带粘弹性项的奇异抛物方程的全局存在性和膨胀解

IF 1.9 3区数学 Q1 MATHEMATICS

Journal of Function Spaces Pub Date : 2024-05-28 DOI:10.1155/2024/5754129

Yanchao Gao, Wenxu Jia, Zhixin Feng

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引用次数: 0

摘要

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

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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来源期刊

Journal of Function Spaces MATHEMATICS, APPLIEDMATHEMATICS -MATHEMATICS

CiteScore

4.10

自引率

10.50%

发文量

451

审稿时长

15 weeks

期刊介绍： Journal of Function Spaces (formerly titled Journal of Function Spaces and Applications) publishes papers on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines. As well as original research, Journal of Function Spaces also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.