The blow-up of solutions of a class of nonlinear viscoelastic Kirchhoff equation with suitable initial data and Dirichlet boundary conditions is discussed. By constructing a suitable auxiliary function to overcome the difficulty of gradient estimation and making use of differential inequality technique, we establish a finite time blow-up result when the initial data is at arbitrary energy level. Moreover, a lower bound of the lifespan is also derived by constructing a control function with both nonlocal term and memory kernel. Compared with the previous literature, our approach to estimate the...
