Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term (Journal of Partial Differential Equations, 2024)
This work considers the initial boundary value problem for a viscoelasticwave equation with a nonlinear boundary source term. Under suitable assumptions,we prove the existence of global weak solutions using the Galerkin approximation.Then, we give a decay rate estimate of the energy by making use of the perturbedenergy method.
Keywords: Viscoelastic equation; nonlinear boundary source; stabilization.