General Decay Rates for a Viscoelastic Wave Equation with Dynamic Boundary Conditions and Past History

Feng, Baowei

doi:10.1007/s00009-018-1154-4

Cited by 14 publications

(7 citation statements)

References 23 publications

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“…They are not only important from the theoretical point of view but also arise in several physical applications (see [9,10,8,1]). In case of M = 1, Feng [7] considered the following viscoelastic wave equation with dynamic boundary conditions…”

Section: Introductionmentioning

confidence: 99%

General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions

Lv¹,

Hao²

2023

MCRF

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<p style='text-indent:20px;'>In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions <inline-formula><tex-math id="M1">\begin{document}$ g_i $\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$ (i = 1, 2, \cdots, l) $\end{document}</tex-math></inline-formula> satisfy <inline-formula><tex-math id="M3">\begin{document}$ g_i(t)\leq-\xi_i(t)G(g_i(t)) $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> is an increasing and convex function near the origin and <inline-formula><tex-math id="M5">\begin{document}$ \xi_i $\end{document}</tex-math></inline-formula> are nonincreasing, we establish some optimal and general decay rates of the energy using the multiplier method and some properties of convex functions. Moreover, we obtain the finite time blow-up result of solution with nonpositive or arbitrary positive initial energy. The results in this paper are obtained without imposing any growth condition on weak damping term at the origin. Our results improve and generalize several earlier related results in the literature.</p>

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Section: Introductionmentioning

confidence: 99%

General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions

Lv¹,

Hao²

2023

MCRF

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“…In Sect.3, we establish the general decay result of the energy. In this paper we will use a lot of concepts and techniques contained in Feng [16].…”

Section: Introductionmentioning

confidence: 99%

Elastic membrane equation with dynamic boundary conditions and infinite memory

Merah

Mesloub

2022

bspm

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“…Wu [22] used this assumption to study a wave Kirchhoff-type wave equation with a boundary control of memory type. For nonlinear wave equations with memorytype boundary condition, we refer to Cavalcanti and Guesmia [23], Feng [24], Feng et al [25][26][27], Muñoz Rivera and Andrade [28], and Zhang [29].…”

Section: Introductionmentioning

confidence: 99%

A New General Decay Rate of Wave Equation with Memory-Type Boundary Control

Fan

2021

Mathematical Problems in Engineering

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Of interest is a wave equation with memory-type boundary oscillations, in which the forced oscillations of the rod is given by a memory term at the boundary. We establish a new general decay rate to the system. And it possesses the character of damped oscillations and tends to a finite value for a large time. By assuming the resolvent kernel that is more general than those in previous papers, we establish a more general energy decay result. Hence the result improves earlier results in the literature.

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General Decay Rates for a Viscoelastic Wave Equation with Dynamic Boundary Conditions and Past History

Cited by 14 publications

References 23 publications

General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions

General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions

Elastic membrane equation with dynamic boundary conditions and infinite memory

A New General Decay Rate of Wave Equation with Memory-Type Boundary Control

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