Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation (Q896480)

In this paper, the author investigates the nonlinear viscoelastic equation with the memory kernel and two different power-like nonlinearities: \[ u_{tt} - \Delta u + \int^t_0 g(t - \tau ) \Delta u(\tau )d\tau + |u_t|^{m-2}u_t = |u| ^{p-2}u \] in the domain \(\Omega \times [0, T]\). A solution \(u(x,t)\) is assumed to satisfy initial conditions and Dirichlet boundary conditions. Here, \(g\) is a nonincreasing positive kernel function. The main goal is to provide conditions on the model parameters guaranteeing the finite time blow up of solutions having high initial energy.