Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022027

M. Alahyane, M. Al‐Gharabli, Adel M. Al-Mahdi

引用次数: 0

Abstract

In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [27], [4], [33], [58] and [34]. The proof is based on the energy method together with convexity arguments. Numerical simulations are given to illustrate the theoretical decay result.

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具有无限记忆的Bresse系统在纵向位移中的理论和计算衰减结果

在本文中，我们考虑一个一维线性Bresse系统，它的第三个方程(纵向位移)中只有一个无限记忆项。在记忆核(松弛函数)的一般条件下，我们建立了系统能量的衰减估计。我们的衰减结果扩展并改进了文献[27]、[4]、[33]、[58]和[34]中得到的一些衰减率。该证明是基于能量法和凸性论证。数值模拟说明了理论的衰减结果。

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