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

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

引用次数: 0

Abstract

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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具有无限记忆效应与超临界摩擦阻尼的波方程能量衰减

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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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

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