Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

Al‐Mahdi, Adel M.

doi:10.1186/s13661-019-1196-y

Cited by 16 publications

(3 citation statements)

References 40 publications

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“…with boundary damping, and they obtained stability results. For more results in this direction, see [3,[26][27][28][29].…”

Section: Plate Problemsmentioning

confidence: 99%

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

Al‐Gharabli

2019

Bound Value Probl

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In this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal condition g (t) ≤-ξ (t)G(g(t)), where ξ and G satisfy some properties. With this very general assumption on the behavior of g, we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when G(s) = s p and p covers the full admissible range [1, 2). Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (

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“…with boundary damping, and they obtained stability results. For more results in this direction, see [3,[26][27][28][29].…”

Section: Plate Problemsmentioning

confidence: 99%

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

Al‐Gharabli

2019

Bound Value Probl

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“…Among several works which deal with viscoelastic equations long-time memory, we refer the reader to a large class of papers on viscoelastic beams [17][18][19][20]. For the stability of viscoelastic equations with a distributed damping term in the domain or on the boundary, we refer to [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

Al‐Gharabli,

Messaoudi

2023

Math Methods in App Sciences

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In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature.

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“…For more recent works regarding nonlinearity, we refer [13][14][15][16][17][18][19][20][21][22][23]. For the relaxation function, Cavalcanti et al [24], reported an exponential decay result using relaxation functions which satisfy, −ξ 2 g(t) ≥ g (t) ≥ −ξ 1 g(t), t ≥ 0.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Theoretical Stability Study of a Viscoelastic Plate Equation with Nonlinear Frictional Damping Term and a Logarithmic Source Term

Al‐Gharabli

Al‐Mahdi

Noor

et al. 2022

MCA

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This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies g′(t)≤−ξ(t)G(g(t)), we establish an explicit general decay rates without imposing a restrictive growth assumption on the damping term. This general condition allows us to recover the exponential and polynomial rates. Our results improve and extend some existing results in the literature. We preform some numerical experiments to illustrate our theoretical results.

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Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

Cited by 16 publications

References 40 publications

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

Numerical and Theoretical Stability Study of a Viscoelastic Plate Equation with Nonlinear Frictional Damping Term and a Logarithmic Source Term

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