非线性波动方程半离散格式的一致指数稳定性OA
On uniform exponential stability of semi-discrete scheme for nonlinear wave equation
本文讨论一维非线性波动方程半离散有限差分格式的一致指数稳定性.首先,利用能量乘子法证明了偏微分方程描述的连续系统的指数稳定性.引入辅助变量,利用降阶法将原系统转化为奇异偏微分方程(PDE)系统;再用有限差分法对空间变量离散,在消除引入的辅助变量后,得到原系统的半离散有限差分格式;最后,平行于连续系统,利用能量乘子法证明了离散系统的一致指数稳定性,并通过数值模拟进行验证.
This paper investigates the uniform exponential stability of semi-discrete finite difference schemes applied to one-dimensional nonlinear wave equations.Firstly,the energy multiplier method is employed to establish the exponential stability of the continuous system governed by the partial differential equation(PDE).This involves introducing auxiliary variables and employing the reduction technique to convert the original system into a singular PDE system.Subsequently,the spatial variable is discretized using the finite difference method,and upon eliminating the auxiliary variables,the semi-discrete finite difference scheme for the original system is derived.Finally,mirroring the approach for the continuous system,the energy multiplier method is utilized to prove the uniform exponential stability of the discrete system,which is further validated through numerical simulations.
王丽梅;郭宝珠
华北电力大学数理学院,北京 102206华北电力大学数理学院,北京 102206||中国科学院数学与系统科学研究院,北京 100190
波动方程半离散有限差分格式能量乘子法降阶法一致指数稳定性
wave equationsemi-discrete finite difference schemeenergy multiplier methodorder reduction methoduniform exponential stability
《控制理论与应用》 2026 (3)
451-459,9
国家自然科学基金项目(12131008)资助.Supported by the National Natural Science Foundation of China(12131008).
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