具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性

刘烁, 张宏伟, 呼青英

doi:10.13371/j.cnki.chin.q.j.m.2021.02.010

数学季刊 >

2021 , Vol. 36 >Issue 2: 210 - 220

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.010

具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性

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Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

LIU Shuo (1996-), female, native of Yanshi, Henan, master student of Henan University of Technology, engages in PDE; ZHANG Hong-wei (1966-), male, native of Fugou, Henan, professor of Henan University of Technology, Ph.D, engages in PDE. Hu Qing-ying (1966-), female, native of Fugou, Henan, professor of Henan University of Technology, Ph.D, engages in PDE.

收稿日期: 2021-01-13

网络出版日期: 2021-03-02

基金资助

Supported by National Natural Science Foundation of China (Grant No.
11801145).

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Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms

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Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

Received date: 2021-01-13

Online published: 2021-03-02

Supported by

Supported by National Natural Science Foundation of China (Grant No.
11801145).

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摘要

This paper is concerned with a system of nonlinear viscoelastic
wave equations with degenerate nonlocal damping and memory terms. We will
prove that the energy associated to the system is unbounded. In fact, it will
be proved that the energy will grow up as an exponential function as time goes
to infinity, provided that the initial data are positive initial energy.

关键词： Exponential growth; Nonlocal damping; Positive initial energy;
Viscoelastic wave equations

本文引用格式

刘烁, 张宏伟, 呼青英 . 具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性[J]. 数学季刊, 2021 , 36(2) : 210 -220 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.010

Abstract

Key words： Exponential growth; Nonlocal damping; Positive initial energy;
Viscoelastic wave equations

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