Mathematical Methods in the Applied Sciences · 2015 · 12 citations · 17 references
Natural SciencesMathematicsDifferential EquationsGravityOptimizationBoundary ConditionsBoundary-value ProblemsExistence TheoryInequalityInitial Value ProblemsPartial Differential EquationsBlow-up CriteriaBoussinesq EquationsCauchy ProblemConcavity AnalysisFinite TimeGlobal Existence TheoryKlein-gordon EquationNonlinear Initial Value Problems
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 and generalized Boussinesq equation is proven. 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. Copyright © 2015 John Wiley & Sons, Ltd.
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