On the decay rate of a Timoshenko system with dual-phase-lag thermoelasticity in unbounded domains

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-04-05 Epub Date: 2026-01-28 DOI:10.1002/mana.70112

Hizia Bounadja, Salim Messaoudi, Maisa Khader

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引用次数: 0

Abstract

In this paper, we investigate the Cauchy problem for a dual-phase-lag (DPL) thermoelastic Timoshenko system with a DPL heat conduction. This DPL model, which includes two thermal relaxation times, $τ_{q}$ and $τ_{θ}$ , describes non-instantaneous heat propagation. We first study the decay properties of the system using the energy method in Fourier space, by constructing an appropriate Lyapunov functional. Then, we prove that the $L^{2}$ -norm of the solution decays with the rate ${(1 + t)}^{- 1 / 8}$ , with some regularity loss and under the assumption $2 τ_{θ} > τ_{q}$ .

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无界域双相滞后热弹性Timoshenko系统的衰减速率

本文研究了具有双相滞后热传导的热弹性Timoshenko系统的Cauchy问题。该DPL模型包含两个热松弛时间τ q $\tau _{q}$和τ θ $\tau _{\theta }$，描述了非瞬时热传播。我们首先通过构造一个适当的Lyapunov泛函，利用傅里叶空间的能量方法研究了系统的衰减特性。然后，我们证明了解的l2 $L^{2}$ -范数以(1 + t)−1 / 8的速率衰减$(1+t)^{-1/8}$，有一定的规律性损失，假设2 τ θ ＆gt； τ q $2\tau _{\theta }>\tau _{q}$。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index