Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
The authors consider the viscoelastic problem with nonlinear boundary damping in a bounded and star-shaped domain of with smooth boundary. The main results are devoted to the global existence of strong and weak solutions of the problem and the uniform decay (either exponential or algebraic) of the energy related to the problem under suitable assumptions. The existence is proved by means of the Faedo-Galerkin method, and the asymptotic behavior is shown by making use of the multiplier technique combined with integral inequalities due to \textit{V. Komornik} [Exact controllability and stabilization. The multiplier method. Research in Applied Mathematics. 36. Chichester: Wiley. Paris: Masson (1994; Zbl 0937.93003)].
scientific article; zbMATH DE number 1832808