Stability for nonlinear wave motions damped by time-dependent frictions

Zhe Jiao; Yong Xu; Lijing Zhao

doi:10.1016/j.cnsns.2022.106965

Stability for nonlinear wave motions damped by time-dependent frictions

Zhe Jiao, Yong Xu, Lijing Zhao

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. It is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein–Gordon equation.

Original language	English
Article number	106965
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	117
DOIs	https://doi.org/10.1016/j.cnsns.2022.106965
State	Published - Feb 2023

Keywords

Convergence to equilibria
Decay rate
Dissipative wave system
Nonautonomous damping

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10.1016/j.cnsns.2022.106965

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title = "Stability for nonlinear wave motions damped by time-dependent frictions",

abstract = "We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. It is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein–Gordon equation.",

keywords = "Convergence to equilibria, Decay rate, Dissipative wave system, Nonautonomous damping",

author = "Zhe Jiao and Yong Xu and Lijing Zhao",

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T1 - Stability for nonlinear wave motions damped by time-dependent frictions

AU - Jiao, Zhe

AU - Xu, Yong

AU - Zhao, Lijing

PY - 2023/2

Y1 - 2023/2

N2 - We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. It is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein–Gordon equation.

AB - We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. It is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein–Gordon equation.

KW - Convergence to equilibria

KW - Decay rate

KW - Dissipative wave system

KW - Nonautonomous damping

UR - http://www.scopus.com/inward/record.url?scp=85141329939&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2022.106965

DO - 10.1016/j.cnsns.2022.106965

M3 - 文章

AN - SCOPUS:85141329939

SN - 1007-5704

VL - 117

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106965

ER -

Stability for nonlinear wave motions damped by time-dependent frictions

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Keywords

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