Blowup for a Damped Wave Equation with Mass and General Nonlinear Memory

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-18 DOI:10.1007/s40840-024-01673-9

Zhendong Feng, Fei Guo, Yuequn Li

引用次数: 0

Abstract

We investigate the blowup conditions to the Cauchy problem for a semilinear wave equation with scale-invariant damping, mass and general nonlinear memory term (see Eq. (1.1) in the Introduction). We first establish a local (in time) existence result for this problem by Banach’s fixed point theorem, where Palmieri’s decay estimates on the solution to the corresponding linear homogeneous equation play an essential role in the proof. We then formulate a blowup result for energy solutions by applying the iteration argument together with the test function method.

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带质量和一般非线性记忆的阻尼波方程的炸裂

我们研究了具有尺度不变阻尼、质量和一般非线性记忆项的半线性波方程（见引言中的公式 (1.1)）的考奇问题的炸毁条件。我们首先通过巴纳赫定点定理建立了该问题的局部（时间）存在性结果，其中 Palmieri 对相应线性均质方程解的衰减估计在证明中起着至关重要的作用。然后，我们通过应用迭代论证和检验函数法，提出了能量解的炸毁结果。

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.