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

摘要

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).