一类强阻尼强延迟一维热弹性III型可磁化压电梁系统解的指数衰减结果

IF 1.8 3区 数学 Q1 MATHEMATICS, APPLIED
Hassan Messaoudi, Sami Loucif, Salah Zitouni
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引用次数: 0

摘要

在本研究中,我们研究了具有强阻尼和强延迟作用于热方程的一维可磁化压电梁系统,其中热传导由Green和Naghdi理论给出。首先,利用半群理论证明了系统是适定的。通过构造适当的Lyapunov泛函,建立了系统解的指数稳定性结果。在关于时滞权重的适当假设下,建立了系统解的指数稳定性。这一假设假设,通过热传导的阻尼效应足以稳定系统,即使在引入时间延迟时也是如此。重要的是,我们的结果的鲁棒性值得注意,因为它不依赖于系统参数之间的任何特定关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Exponential Decay Results of Solutions for a One-Dimensional Magnetizable Piezoelectric Beam System of Thermoelasticity of Type III With Strong Damping and a Strong Delay

Exponential Decay Results of Solutions for a One-Dimensional Magnetizable Piezoelectric Beam System of Thermoelasticity of Type III With Strong Damping and a Strong Delay

In this research work, we study a one-dimensional magnetizable piezoelectric beam system with strong damping and a strong delay acting on the heat equation, where the heat conduction is given by Green and Naghdi theory. First, we establish by exploiting the semigroup theory that the system is well-posed. Through the construction of an appropriate Lyapunov functional, we establish the exponential stability result for the solutions of the system. The exponential stability of the system's solutions is established under a pertinent assumption regarding the weight of the delay. This assumption posits that the damping effect through heat conduction is sufficiently potent to stabilize the system, even when a time delay is introduced. Importantly, the robustness of our result is noteworthy, as it does not hinge on any specific relationships among system parameters.

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来源期刊
CiteScore
4.90
自引率
6.90%
发文量
798
审稿时长
6 months
期刊介绍: Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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