Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term (Journal of Partial Differential Equations, 2020)
We are interested in the study of a coupled systemof viscoelasticwave equations with a delay term. Firstly global existence of the solutions is proved. The asymptotic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature.
Keywords: Global existence; energy decay; nonlinear damping