Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay

被引：1

作者：

Boukhari, Boumediene ^{[1
]}

Mtiri, Foued ^{[2
]}

Bchatnia, Ahmed ^{[3
]}

Beniani, Abderrahmane ^{[1
]}

机构：

[1] Univ Ain Temouchent, Fac Sci & Technol, Dept Math, Engn & Sustainable Dev Lab, Ain Temouchent 46000, Algeria

[2] King Khalid Univ, Appl Coll Mahayil, Dept Math, Abha, Saudi Arabia

[3] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, LR Anal Nonlineaire & Geometrie,LR21ES08, Tunis 2092, Tunisia

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 11期

关键词：

Euler-Bernoulli beam equation; dynamic boundary dissipation of fractional derivative type; frequency domain method; strong stability; DISSIPATION; EQUATIONS;

D O I：

10.3934/math.20241541

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper analyzes an Euler-Bernoulli beam equation in a bounded domain with a boundary control condition involving a fractional derivative. By utilizing the semigroup theory of linear operators and building on the results of Borichev and Tomilov, the stability properties of the system are examined. Additionally, a numerical scheme is developed to reproduce various decay rate behaviors. The numerical simulations confirm the theoretical stability results regarding the energy decay rate and demonstrate exponential decay for specific configurations of initial data.

引用

页码：32102 / 32123

页数：22

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