Stabilization and Discretization of the Coupled Heat and Wave Equations

4区 工程技术 Q1 Mathematics Mathematical Problems in Engineering Pub Date : 2023-12-27 DOI:10.1155/2023/8901825
Kun-Yi Yang, Xu Zhang
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Abstract

In this paper, we consider the stabilization of the coupled heat and wave equations under the static feedback or the dynamic feedback. Moreover, we make the coupled systems discretized by using the finite-volume approach, and then we consider the stabilized properties of the discrete systems. First, for the coupled system under the static feedback, it is shown that the system is exponentially stable by using the Lyapunov method, and then the corresponding discrete system can be shown to be exponentially stable by constucting the discretized Lyapunov function. Second, for the coupled system under the dynamic feedback, we also show that both of the system and its discrete scheme are exponentially stable. Third, numerical simulations are given to show the effectiveness of the stable controllers.
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热方程和波方程耦合的稳定化和离散化
本文考虑了热方程和波方程在静态反馈或动态反馈下的稳定问题。此外,我们利用有限体积方法将耦合系统离散化,然后考虑离散系统的稳定化特性。首先,对于静态反馈下的耦合系统,利用李亚普诺夫方法证明系统是指数稳定的,然后通过构造离散化的李亚普诺夫函数可以证明相应的离散系统是指数稳定的。其次,对于动态反馈下的耦合系统,我们也证明了系统及其离散方案都是指数稳定的。第三,我们给出了数值模拟,以显示稳定控制器的有效性。
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来源期刊
Mathematical Problems in Engineering
Mathematical Problems in Engineering 工程技术-工程:综合
CiteScore
4.00
自引率
0.00%
发文量
2853
审稿时长
4.2 months
期刊介绍: Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.
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