General decay for a viscoelastic equation of variable coefficients with a time-varying delay in the boundary feedback and acoustic boundary conditions

2017 ◽  
Vol 37 (5) ◽  
pp. 1453-1471 ◽  
Author(s):  
Yamna BOUKHATEM ◽  
Benyattou BENABDERRAHMANE
Keyword(s):  
Boundary Conditions ◽  
Variable Coefficients ◽  
General Decay ◽  
Time Varying ◽  
Acoustic Boundary Conditions ◽  
Time Varying Delay ◽  
Boundary Feedback ◽  
Viscoelastic Equation ◽  
Varying Delay

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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