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

LIU Shuo, ZHANG Hong-wei, Hu Qing-ying

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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.

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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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

Cite this article

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

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