Global nonexistence for nonlinear Kirchhoff systems with memory term

Abstract

The initial boundary value problem for nonlinear wave equations of Kirchhoff systems with memory type in a bounded domain is considered. By modifying the method introduced in a work by Autuori et al. (Arch Rational Mech Anal 196:489-516, 2010), we establish the nonexistence result of global solutions with the initial energy controlled above by a critical value, that is, when the initial data belong to a specific region in the phase plane. This improves earlier results in the literatures.