Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary Original Research Article

We consider a nonlinear wave equation of Kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.