Revised Concavity Method and Application to Klein-Gordon Equation

Milena Dimova, Natalia Kolkovska, Nikolai Kutev


A revised version of the concavity method of Levine, based on a new ordinary differential inequality, is proposed. Necessary and sufficient condition for nonexistence of global solutions of the inequality is proved. As an application, finite time blow up of the solution to Klein-Gordon equation with arbitrary positive initial energy is obtained under very general structural conditions.

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