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MSC: 35B35, 35B40, 35L70
Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq equation
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.
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