This paper deals with the blow-up problem for equation \[ u_{tt}-\Delta u-\omega\Delta u_t+\mu u_t = |u|^{p-2}u, \] where \((x,t)\in\Omega\times\mathbb{R}_+^*\), with Dirichlet boundary conditions, with \(\omega\geq 0\), and \(\mu\geq 0\). Here, \(\Omega\) is a smooth bounded domain of \(\mathbb{R}^n\) (\(n\geq 1\)), and \(p>2\) if \(n\leq 2\), \(p\in(2, 2n/(n-2)]\) if \(n\geq 3\) and \(\omega>0\), and \(p\in(2, 2(n-1)/(n-2)]\) if \(n\geq 3\) and \(\omega=0\). The main result states that solutions blow-up in finite time if the \(L^2\)-scalar product of the Cauchy data \(u_0\) and \(u_1\) is large enough for \(t=0\) (see eq. (9) of the paper). The paper relies on a paper by F. Gazzola and M. Squassina [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 2, 185–207 (2006; Zbl 1094.35082)] on this equation.