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Keywords:
Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq equation
Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq 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.
References:
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