Asymptotic stability for nonlinear Kirchhoff systems

We study the asymptotic stability for solutions of the nonlinear damped Kirchhoff system, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force ff and the distributed damping QQ. Then the results are extended to a more delicate problem involving also an internal dissipation of higher order, the so called strongly damped Kirchhoff system. Finally, the study is further extended to strongly damped Kirchhoff–polyharmonic systems, which model several interesting problems of the Woinowsky–Krieger type.