BLOW-UP RESULTS FOR SOME NONLINEAR HYPERBOLIC PROBLEMS

We study the nonexistence of global solutions for equations and inequalities of the following type tt u≥ΔA(x,t,u) + B(x,t,u) on R+N+1 with nonlinearity on A and B of the form A(x,t,u) = ρ1(x,t) |u|p , B(x,t,u) = ρ2 (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.