控制理论与应用2026，Vol.43Issue(3)：451-459,9.DOI:10.7641/CTA.2024.40160
非线性波动方程半离散格式的一致指数稳定性
On uniform exponential stability of semi-discrete scheme for nonlinear wave equation
摘要
Abstract
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.关键词
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Key words
wave equation/semi-discrete finite difference scheme/energy multiplier method/order reduction method/uniform exponential stability引用本文复制引用
王丽梅,郭宝珠..非线性波动方程半离散格式的一致指数稳定性[J].控制理论与应用,2026,43(3):451-459,9.基金项目
国家自然科学基金项目(12131008)资助.Supported by the National Natural Science Foundation of China(12131008). （12131008）
