具有局部边界分数耗散的耦合波方程解的能量多项式衰减

IF 1.5 3区数学 Q1 MATHEMATICS Journal of Inequalities and Applications Pub Date : 2024-09-12 DOI:10.1186/s13660-024-03200-7

Amina Chaili, Abderrahmane Beniani, Ahmed Bchatnia, Suleman Alfalqi

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引用次数: 0

摘要

在本文中，我们研究了一个耦合波方程系统，该系统的特点是对部分域施加边界分数阻尼。我们首先建立了该系统的良好拟合性，并通过半群理论证明了解的存在性和唯一性。虽然该系统没有表现出指数稳定性，但我们证明了其强大的稳定性。此外，利用阿伦特和巴蒂的一般标准以及某些几何条件，我们证明了解的多项式能量衰减率。

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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Polynomial decay of the energy of solutions of coupled wave equations with locally boundary fractional dissipation

In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.