Department of Mathematical Modeling and Numerical Analysis
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well-known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein-Gordon equation is proved. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being.