Exponential decay of non‐linear wave equation with a viscoelastic boundary condition

“…Wu 11 used this assumption to study a Kirchhoff-type wave equation. Please see previous studies, [12][13][14][15][16][17][18][19] etc., for the results on wave equations with boundary condition of memory type.…”

Section: Introductionmentioning

confidence: 99%

Memory‐type boundary stabilization of a transmission problem for Kirchhoff wave equations

Fan

Feng

2022

Math Methods in App Sciences

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In this paper, we consider a transmission problem for Kirchhoff-type wave equations with boundary condition determined by the long-range memory. The wave propagation over bodies consisting of two physically different types of materials. One component is clamped, and the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. Under a wider assumption of the kernel, we establish a more general decay rate of energy, which improves earlier results established in the literature.

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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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Exponential decay of non‐linear wave equation with a viscoelastic boundary condition

Cited by 4 publications

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Decaimiento Exponencial De Una Ecuación De Onda Con Una Condición De Frontera Viscoelástica Y Un Término Fuente

Decaimiento Exponencial De Una Ecuación De Onda Con Una Condición De Frontera Viscoelástica Y Un Término Fuente

Memory‐type boundary stabilization of a transmission problem for Kirchhoff wave equations

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

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