Asymptotic Behavior of Solutions of Some Viscoelastic Problems

Hamdi, Soumia (2024) Asymptotic Behavior of Solutions of Some Viscoelastic Problems. Doctoral thesis, Université Mohamed Khider (Biskra - Algérie).

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Abstract

The main purpose of this thesis is to investigate the existence and uniqueness of solutions, as well as the asymptotic behavior of some viscoelastic problems in one-dimensional space, precisely, this work addresses the problem of undesirable vibrations and the control of attitude stabilization of a flexible satellite during the maneuvers. In view of this, viscoelastic materials are suggested to attenuate or suppress the unwanted vibrations of a flexible satellite. The flexible satellite system consists of a central rigid hub and two large symmetric flexible appendages. Mathematically, the problem can be modeled by a set of partial differential equations (PDEs) taking into account the dynamic boundary condition. Our research utilizes Lyapunov’s direct method to study some viscoelastic systems. The results obtained in this thesis aim to enhance much of the previous scientific research.

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