Blow-up results for some nonlinear hyperbolic problems

We study the nonexistence of global solutions for equations and inequalities of the following type $\partial_{tt}u\ge\Delta A(x,t,u)+ B(x,t,u)$ on $\bbfR^{N+1}_+$ with nonlinearity $A$ and $B$ of the form $A(x,t,u)=\rho_1(x,t)|u|^p$, $B(x,t,u) =\rho_2(x,t)|u|^q$. We also study the nonexistence for some more general inequalities of second-order but without any assumption about the type of operator. The method relies on a suitable choice of test functions, rescaling techniques and a dimensional analysis.