时齐马氏链渐进性双曲方程稳定解存在性分析

Analysis of Hyperbolic Equations Stable Solutions Based on Time Homogeneous Markov Chain Progressive

双曲方程的稳定解分析方法在现代数学应用中具有广泛的意义。采用时齐马氏链进行双曲方程稳定解存在性分析具有模型匹配度高的优点。构建时齐马氏链的双曲波动方程,设计自组织非光滑时滞的双曲系统,结合时齐马氏链渐进性条件下的Lyapunov-Krasovskii泛函算法,对时齐马氏链渐进性条件临界阈值确定,以有效分析双曲方程的稳定解存在性,提高并行算法处理效率,在一阶非光滑时滞系统中得到方向性时齐马氏链函数的分解特征。研究证明,时齐马氏链渐进性条件下,双曲方程存在稳定性解,解向量在有限时间内收敛。

Stable solutions analysis method is significant in modern mathematics application solutions to hyperbolic equa-tion stability. Using homogeneous Markov chain analysis of the existence of stable solutions of hyperbolic equations withmodel construction, and the matching rate is high. The hyperbolic wave equation of homogeneous Markov chain is construct-ed, the self organization design of non smooth delay hyperbolic systems are obtained, combined with Markov chain progres-sive Lyapunov-Krasovskii functional conditions, time homogeneous Markov chain progressive condition critical thresholdis determined, it can effectively analyze hyperbolic equations stable existence of parallel algorithm, improve processing effi-ciency. In order to get non smooth systems with time-delay are directional decomposition of homogeneous Markov chainfunction. Research shows that the time homogeneous Markov chain progressive condition is taken, it has existence and sta-bility for hyperbolic partial differential equations, the solution vector convergence is shown in finite time.