We consider a viscoelastic wave equation with weak, strong damping and power nonlinearity. We have already obtained a global solution and its decay rate in . In this paper, we apply the concavity method in order to show that the solution blows up in finite time under non-classic constraint on $\mu$.
"Finite time blow-up for a viscoelastic wave equation with weak-strong damping and power nonlinearity." Osaka J. Math. 58 (3) 661 - 669, July 2021.