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

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
文章编号	106965
期刊	Communications in Nonlinear Science and Numerical Simulation
卷	117
DOI	https://doi.org/10.1016/j.cnsns.2022.106965
出版状态	已出版 - 2月 2023

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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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year = "2023",

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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

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U2 - 10.1016/j.cnsns.2022.106965

DO - 10.1016/j.cnsns.2022.106965

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VL - 117

JO - Communications in Nonlinear Science and Numerical Simulation

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M1 - 106965

ER -

Stability for nonlinear wave motions damped by time-dependent frictions

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