具有无限记忆效应与超临界摩擦阻尼的波方程能量衰减

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-11 DOI:10.1007/s11587-023-00832-7

Menglan Liao

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引用次数: 0

摘要

本文考虑了有界域 $\Omega \subset {\mathbb {R}}^3$ 中的一类阻尼粘弹性波方程 $$begin{aligned}u_{tt}-k(0)\Delta u-\int _0^\infty k'(s)\Delta u(t-s)ds+|u_t|^{m-1}u_t=|u|^{p-1}u \end{aligned}$$。在之前的工作（Guo et al., Z Angew Math Phys 69:65, 2018）中，针对$1\le m\le 5$讨论了取决于弛豫函数$-k'(s)$的均匀能量衰减。根据马丁内斯（ESAIM Control Optim Calc Var 4:419-444，1999）获得的关键积分不等式，我们建立了对\（m>5\ ）总能量的衰变估计。我们的结果改进并补充了之前的结果。作为一个例子，我们还提出了对数能量衰减。

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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Energy decay of wave equations with infinite memory effects versus supercritical frictional dampings

In this paper, a class of damped viscoelastic wave equations

$$\begin{aligned} u_{tt}-k(0)\Delta u-\int _0^\infty k'(s)\Delta u(t-s)ds+|u_t|^{m-1}u_t=|u|^{p-1}u \end{aligned}$$

is considered in a bounded domain $\Omega \subset {\mathbb {R}}^3$. Uniform energy decay was discussed which depends on the relaxation function $-k'(s)$ in the previous work (Guo et al., Z Angew Math Phys 69:65, 2018) for $1\le m\le 5$. Depending on a key integral inequality obtained by Martinez (ESAIM Control Optim Calc Var 4:419–444, 1999), we establish the decay estimate of the total energy for $m>5$. Our results improve and complement the previous one. As an example, a logarithmic energy decay is also presented.

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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.