Global nonexistence of solution for coupled nonlinear Klein-Gordon with degenerate damping and source terms

Ouchenane, Djamel; Khalili, Zineb; Yazid, Fares

doi:10.24193/subbmath.2022.4.10

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Then they demonstrated the plynomial decay and optimality. For comprehensive insights, refer to references [5,7,12,13,16]. Inspiriting by previous work, in our article, we study the Timoshenko system below with a strong damping and a strong distributed delay when it acts on the first equation:…”

Section: Introductionmentioning

confidence: 97%

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Laribi,

Krelifa,

Zitouni

et al. 2023

Preprint

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In this research work, we study the linear Timoshenko problem with a strong damping and a strong distributed delay when it acts on the first equation. We first prove the existence and uniqueness solution of the system by using the semi-group theory. Then, we illustrate the lack of exponential stability even in the condition of equal wave propagation is satisfied. Furthermore, we show the polynomial decay of solution with rate t−½. From this perspective, we demonstrate the optimality of the rate.

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Section: Introductionmentioning

confidence: 97%

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Laribi,

Krelifa,

Zitouni

et al. 2023

Preprint

Self Cite

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“…General models for frictional contact with wear can be found in [33,42] as well as in survey [41]. The mathematical analysis of various models of frictional contact with wear, including existence and uniqueness results of the weak solution, was carried out in [20], [21], [23], [25], [29]. Thermo-mechanic contact problems with the evolution of the temperature parameter with wear were treated in [5,12,13,36,37,38,39,40].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a thermo-elasto-viscoplastic contact problem with wear and damage

Chouia,

Azeb Ahmed,

Yazid

2023

Ufimsk. Mat. Zh.

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This paper presents a quasistatic problem of a thermo-elaso-visco-plastic body in frictional contact with a moving foundation. The contact is modelled with the normal compliance condition and the associated law of dry friction. The model takes into account wear of the contact surface of the body caused by the friction and which is described by the Archard law. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. We list the assumptions on the data and derive a variational formulation of the mechanical problem. Existence and uniqueness of the weak solution for the problem is proved using the theory of evolutionary variational inequalities, parabolic variational inequalities, first order evolution equation and Banach fixed point.

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A blow‐up result of a nonlinear viscoelastic wave equations system with variable dampings and sources

Laribi,

Krelifa,

Zitouni

et al. 2024

Math Methods in App Sciences

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This quest paper covers the most important topic in the field of mechanics. It is the nonlinear viscoelastic wave equations with variable degenerate damping and sources acting in both equations. We seek to prove that this system has no solution with positive initial energy. So, to establish our goal, we utilize the methods and techniques used by Said‐Houari in (J. Nonlinear. Differ. Equ. Appl, vol. 18, 2011, pp. 659‐684.).

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Global nonexistence of solution for coupled nonlinear Klein-Gordon with degenerate damping and source terms

Abstract: "In this article we consider a coupled system of nonlinear Klein-Gordon equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solutions by concavity method."

Cited by 4 publications

References 17 publications

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Analysis of a thermo-elasto-viscoplastic contact problem with wear and damage

A blow‐up result of a nonlinear viscoelastic wave equations system with variable dampings and sources

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