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

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

数学季刊 ›› 2021, Vol. 36 ›› Issue (2): 210-220.doi: 10.13371/j.cnki.chin.q.j.m.2021.02.010

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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

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

收稿日期:2021-01-13 出版日期:2021-06-30 发布日期:2021-04-27
作者简介: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.
基金资助:
Supported by National Natural Science Foundation of China (Grant No.
11801145).

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

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

Received:2021-01-13 Online:2021-06-30 Published:2021-04-27
About author: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.
Supported by:
Supported by National Natural Science Foundation of China (Grant No.
11801145).

摘要/Abstract

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

Abstract: 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.

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

中图分类号:

O175.27

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.

LIU Shuo, ZHANG Hong-wei, Hu Qing-ying. Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(2): 210-220.

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

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

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