Energy Decay of the Solution for a Weak Viscoelastic Equation with a Time-Varying Delay

2017 ◽  
Vol 155 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Gongwei Liu ◽  
Lin Diao
Keyword(s):  
Energy Decay ◽  
Time Varying ◽  
Time Varying Delay ◽  
Viscoelastic Equation ◽  
Varying Delay

scholarly journals Asymptotic stability of a viscoelastic problem with time-varying delay in boundary feedback

2021 ◽  
pp. 3-3
Author(s):  
Abita Rahmoune
Keyword(s):  
Feedback Condition ◽  
Time Varying ◽  
Decay Estimates ◽  
Viscoelastic Problem ◽  
Dissipative Term ◽  
Time Varying Delay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation ◽  
The Given ◽  
Varying Delay

In this paper, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.

scholarly journals Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Zaiyun Zhang ◽  
Jianhua Huang ◽  
Zhenhai Liu ◽  
Mingbao Sun
Keyword(s):  
Positive Answer ◽  
Time Varying ◽  
Boundary Stabilization ◽  
Delay Effect ◽  
Time Varying Delay ◽  
Boundary Feedback ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation ◽  
Dissipative Boundary ◽  
Varying Delay

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 Kirane and Said-Houari (2011) and Ammari et al. (2010). Moreover, we give an positive answer to the open problem given by Kirane and Said-Houari (2011).

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