Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback
Summary: 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 [\textit{M. Kirane} and \textit{B. Said-Houari}, Z. Angew. Math. Phys. 62, No. 6, 1065--1082 (2011; Zbl 1242.35163)] and [\textit{K. Ammari} et al., Syst. Control Lett. 59, No. 10, 623--628 (2010; Zbl 1205.93126)]. Moreover, we give an positive answer to the open problem given by Kirane and Said-Houari [loc. cit.].
scientific article; zbMATH DE number 7021736
scientific article