Robin型边界阻尼波动方程的一致指数稳定逼近

刘建康,李欢欢

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (4) : 599-611.

PDF(554 KB)
PDF(554 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (4) : 599-611. DOI: 10.12341/jssms13840
论文

Robin型边界阻尼波动方程的一致指数稳定逼近

    刘建康,李欢欢
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Semi-Discretized Approximation for Uniformly Exponential Stability of Wave Equation with Damped Robin Boundary

    LIU Jiankang, LI Huanhuan
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摘要

对一维Robin型边界阻尼波动方 程构造了一个新的等距网格上的半离散有限差分格式, 该格式 没有数值粘性项, 且可以保持系统的一致指数稳定性. 通过引进一个新的辅助函数, 利用Lyapunov函数方法证明了半 离散格式的一致指数稳定性. 数值实验验证了理论结果.

Abstract

A new semi-discrete finite difference scheme on equidistant grids is proposed for one-dimensional wave equation with damped Robin boundary, which does not need any numerical viscosity terms and preserves the uniformly exponential stability of continuous system. The Lyapunov function method is adopted to prove the uniformly exponential stability of semi-discrete scheme by introducing a new auxiliary function.

关键词

Robin阻尼边界 / 有限差分 / Lyapunov函数 / 一致指数稳定.

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刘建康 , 李欢欢. Robin型边界阻尼波动方程的一致指数稳定逼近. 系统科学与数学, 2020, 40(4): 599-611. https://doi.org/10.12341/jssms13840
LIU Jiankang , LI Huanhuan. Semi-Discretized Approximation for Uniformly Exponential Stability of Wave Equation with Damped Robin Boundary. Journal of Systems Science and Mathematical Sciences, 2020, 40(4): 599-611 https://doi.org/10.12341/jssms13840
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