Global existence and energy decay of solutions to a viscoelastic wave equation with a delay term in the non-linear internal feedback

Benaissa, Abbès; Benguessoum, Aissa; Messaoudi, Salim A.

doi:10.1504/ijdsde.2014.067080

Cited by 17 publications

(15 citation statements)

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“…Benaissa et al [7] considered the case of constant time delay τ, with l � 0 and M(r) � 1. ey proved the global existence and uniform decay for the following problem:…”

Section: Introductionmentioning

confidence: 99%

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

2020

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In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature.

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“…Benaissa et al [7] considered the case of constant time delay τ, with l � 0 and M(r) � 1. ey proved the global existence and uniform decay for the following problem:…”

Section: Introductionmentioning

confidence: 99%

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

2020

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“…Benaissa & Benguessoum [5] investigated the existence and decay properties of solutions to the viscoelastic wave equation with a delay term in the nonlinear internal feedback of the form…”

Section: Introductionmentioning

confidence: 99%

On a Kelvin--Voigt Viscoelastic Wave Equation with Strong Delay

Demchenko¹,

Anikushyn²,

Pokojovy³

2019

SIAM J. Math. Anal.

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An initial-boundary value problem for a viscoelastic wave equation subject to a strong timelocalized delay in a Kelvin & Voigt-type material law is considered. Transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued C 0-and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using the Lyapunov's indirect method. The singular limit τ → 0 is further studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.

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“…For τ (t) = τ 0 , system (1) has been investigated recently by many authors, where they showed the well-posedness and stabilities results in bounded/unbounded domains (see [1], [2], [3], [5], [7], and so on). Concerning the existence and uniqueness result, we refer the reader to read the existing works which is not our aim interesting here (see [10], Theorem 3.1).…”

Section: Introduction and Position Of Problemmentioning

confidence: 99%

Uniform decay for a viscoelastic wave equation with density and time-varying delay in Rn

Zitouni

Zennir

Bouzettouta

2019

Filomat

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Global existence and energy decay of solutions to a viscoelastic wave equation with a delay term in the non-linear internal feedback

Cited by 17 publications

References 0 publications

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

On a Kelvin--Voigt Viscoelastic Wave Equation with Strong Delay

Uniform decay for a viscoelastic wave equation with density and time-varying delay in Rn

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