Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback
type: Item
instance of: scholarly article
title: Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback
zbMATH Open document ID: 1470.93131
DOI: 10.1155/2014/102594
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We investigate a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback. Under suitable assumptions on the relaxation function and time-varying delay effect together with nonlinear dissipative boundary feedback, we prove the global existence of weak solutions and asymptotic behavior of the energy by using the Faedo-Galerkin method and the perturbed energy method, respectively. This result improves earlier ones in the literature, such as [\textit{M. Kirane} and \textit{B. Said-Houari}, Z. Angew. Math. Phys. 62, No. 6, 1065--1082 (2011; Zbl 1242.35163)] and [\textit{K. Ammari} et al., Syst. Control Lett. 59, No. 10, 623--628 (2010; Zbl 1205.93126)]. Moreover, we give an positive answer to the open problem given by Kirane and Said-Houari [loc. cit.].
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 7021736
author: Zai-Yun Zhang
author: Jian Hua Huang
author: Zhenhai Liu
author: Mingbao Sun
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/102594
OpenAlex ID: W2008998871
Wikidata QID: Q59035202
cites work: Feedback boundary stabilization of wave equations with interior delay
cites work: Global existence and general decay for a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density
cites work: Global existence and uniform decay for wave equation with dissipative term and boundary damping
cites work: Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping
cites work: Estimate on the dimension of global attractor for nonlinear dissipative Kirchhoff equation
cites work: Asymptotic stability of the wave equation on compact surfaces and locally distributed damping-A sharp result
cites work: Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: A sharp result
cites work: Q4530284
cites work: Q4816727
cites work: Frictional versus Viscoelastic Damping in a Semilinear Wave Equation
cites work: A note on decay properties for the solutions of a class of partial differential equation with memory
cites work: General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms
cites work: Uniform decay of solutions for a quasilinear system of viscoelastic equations
cites work: General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source
cites work: Q3626733
cites work: General decay of solutions of a nonlinear system of viscoelastic equations
cites work: Exponential or polynomial decay of solutions to a viscoelastic equation with nonlinear localized damping
cites work: Global existence and uniform decay for a nonlinear viscoelastic equation with damping
cites work: General decay of energy for a viscoelastic equation with nonlinear damping
cites work: Global existence and asymptotic behavior for a coupled hyperbolic system with localized damping
cites work: Energy decay rate for a coupled hyperbolic system with nonlinear damping
cites work: Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
cites work: Exponential and polynomial decay for a quasilinear viscoelastic equation
cites work: Exponential decay for a viscoelastic problem with a singular kernel
cites work: Existence and decay of solutions of a viscoelastic equation with a nonlinear source
cites work: General decay of the solution energy in a viscoelastic equation with a nonlinear source
cites work: Asymptotic behavior of solutions of time-delayed Burgers' equation
cites work: Stability analysis of Euler‐Bernoulli beam with input delay in the boundary control
cites work: Not All Feedback Stabilized Hyperbolic Systems are Robust with Respect to Small Time Delays in Their Feedbacks
cites work: An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
cites work: Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
cites work: Stabilization of the wave equation with boundary or internal distributed delay.
cites work: Stabilization of wave systems with input delay in the boundary control
cites work: Feedback stabilization of a class of evolution equations with delay
cites work: Exponential stability of the wave equation with boundary time-varying delay
cites work: Existence and asymptotic stability of a viscoelastic wave equation with a delay
cites work: Method of Lyapunov functionals construction in stability of delay evolution equations
cites work: Stability analysis of heat flow with boundary time-varying delay effect
cites work: Q2995048
cites work: Stability of the heat and of the wave equations with boundary time-varying delays
cites work: Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks
cites work: Stabilization of Second Order Evolution Equations with Unbounded Feedback with Time-Dependent Delay
cites work: Stabilization of second order evolution equations with unbounded feedback with delay
cites work: Q5890172
cites work: Q4828519
description: scientific article; zbMATH DE number 7021736