Stability of a damped wave equation on an infinite star-shaped network

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI:10.3934/eect.2022024

Ahmed Bchatnia, Amina Boukhatem

引用次数: 1

Abstract

In this paper, we study the stability of an infinite star-shaped network of a linear viscous damped wave equation. We prove that, under some conditions, the whole system is asymptotically stable. Moreover we give a decay rate of the energy of the solution. Our technique is based on a frequency domain method.

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无限星形网络上阻尼波动方程的稳定性

<p style='text-indent:20px;'>本文研究了线性粘性阻尼波动方程的无限星形网络的稳定性。证明了在某些条件下，整个系统是渐近稳定的。此外，我们给出了溶液能量的衰减率。我们的技术是基于频域方法。<

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology