Kirchhoff Systems with nonlinear source and boundary damping terms

Abstract. In this paper we treat the question of the non–existence of global solutions, or their long time behavior, of nonlinear hyperbolic Kirchhoff systems. The main p–Kirchhoff operator may be affected by a perturbation and the systems also involve an external force f and a nonlinear boundary damping Q. When p = 2, we consider some problems involving a higher order dissipation term, under dynamic boundary conditions. Special subcases of f and Q, interesting in applications, are presented in Sections 4, 5 and 6.