Remarks on the qualitative behavior of the undamped Klein-Gordon equation

summary:We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature