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

Abstract EN

We investigate a nonlinear viscoelastic equation withinterior 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, weprove the global existence of weak solutions and asymptotic behavior ofthe energy by using the Faedo-Galerkin method and the perturbed energymethod, 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 openproblem given by Kirane and Said-Houari (2011).