In this paper, we consider a system of two wave equations of Kirchhoff with coupled nonlinear and memory conditions at the boundary, and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decays with the same rate of decay of the relaxation functions; that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially.
"Stability for a system of wave equations of Kirchhoff with coupled nonlinear and boundary conditions of memory type." Adv. Differential Equations 8 (7) 873 - 896, 2003. https://doi.org/10.57262/ade/1355926815