General decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions

Park, Sun‐Hye; Kang, Jum-Ran

doi:10.1186/s13661-017-0820-y

Cited by 5 publications

(6 citation statements)

References 24 publications

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“…Proof of Theorem 3.1, case 1, G is linear We multiply (53) by the nonincreasing function σ (t). We use (14), (30) and (66), and invoke (14) to have…”

Section: Proofs Of Our Main Resultsmentioning

confidence: 99%

“…Proof Using L (t) = NE (t) + N 1 ψ 1 (t) + n 0 E (t), combining (30) and (36), using the properties of r i and r i given in Assumption (A3) and using | m • ν |≤ R, we obtain…”

Section: Lemma 47 Under Assumptions (A1)-(a3) the Functional L(t)mentioning

confidence: 99%

“…Furthermore, he showed that the decay rates of the energy are the same rates of decay of the kernel k. However, the decay rate is not necessarily of exponential or polynomial decay type. After that, different papers appeared and used the condition (6) where p = 1; see, for instance, [21][22][23][24][25][26][27][28][29][30]. Lasiecka and Tataru [31] took one step forward and considered the following condition:…”

Section: Introductionmentioning

confidence: 99%

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

Al‐Mahdi

2019

Bound Value Probl

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In this paper, we consider plate equations with viscoelastic damping localized on a part of the boundary and nonlinear damping in the domain. We establish general and optimal decay rate results for a wider class of relaxation functions. These results are obtained without imposing any restrictive growth assumption on the frictional damping term. Our results are more general than the earlier results.

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“…Proof of Theorem 3.1, case 1, G is linear We multiply (53) by the nonincreasing function σ (t). We use (14), (30) and (66), and invoke (14) to have…”

Section: Proofs Of Our Main Resultsmentioning

confidence: 99%

“…Proof Using L (t) = NE (t) + N 1 ψ 1 (t) + n 0 E (t), combining (30) and (36), using the properties of r i and r i given in Assumption (A3) and using | m • ν |≤ R, we obtain…”

Section: Lemma 47 Under Assumptions (A1)-(a3) the Functional L(t)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Al‐Mahdi

2019

Bound Value Probl

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“…Systems with time-varying delays have been extensively considered by many authors (see [16][17][18][19][20][21][22] and references therein). Recently, Zennir [23] considered the stability for solutions of plate equations with a time-varying delay and weak viscoelasticity in R n .…”

Section: Introductionmentioning

confidence: 99%

General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions

Lee,

Kang

2023

Mathematics

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This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a2>0 and without imposing any restrictive growth assumption on the damping term f1, using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function ψ, namely ψ′(t)≤−μ(t)G(ψ(t)), where G is a convex and increasing function near the origin, and μ is a positive nonincreasing function. Moreover, the energy decay rates depend on the functions μ and G, as well as the function F defined by f0, which characterizes the growth behavior of f1 at the origin.

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“…For some positive constant d i , i = 0, 1, 2. Park et al [12] obtained a general decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions. Motivated by the work of Lasiecka and Tatar [13], where a wave equation with frictional damping was considered, another step forward was taken by considering relaxation functions satisfying…”

Section: Introductionmentioning

confidence: 99%

Existence and General Decay of Solutions for a Weakly Coupled System of Viscoelastic Kirchhoff Plate and Wave Equations

Hajjej

2023

Symmetry

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In this paper, a weakly coupled system (by the displacement of symmetric type) consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain is considered. Under the assumptions on a more general type of relaxation functions, an explicit and general decay rate result is established by using the multiplier method and some properties of the convex functions.

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General decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions

Abstract: We consider a weak viscoelastic Kirchhoff plate model with time-varying delay in the boundary. By using a suitable energy and Lyapunov function, we obtain a decay rate for the energy, which depends on the behavior of g and α.

Cited by 5 publications

References 24 publications

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

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

General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions

Existence and General Decay of Solutions for a Weakly Coupled System of Viscoelastic Kirchhoff Plate and Wave Equations

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