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).

scholarly journals Global Existence and Decay of Solutions for Coupled Nondegenerate Kirchhoff System with a Time Varying Delay Term

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Nadia Mezouar ◽  
Salah Mahmoud Boulaaras ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Global Existence ◽  
Stability Estimate ◽  
Time Varying ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Nonlinear Viscoelastic ◽  
Decay Of Solutions ◽  
Weight Condition ◽  
Varying Delay

This paper deals with the global existence of solutions in a bounded domain for nonlinear viscoelastic Kirchhoff system with a time varying delay by using the energy and Faedo–Galerkin method with respect to the delay term weight condition in the feedback and the delay speed. Furthermore, by using some convex functions properties, we prove a uniform stability estimate.

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