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Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations
Author(s) -
Kutev Nikolay,
Kolkovska Natalia,
Dimova Milena
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3639
Subject(s) - mathematics , ordinary differential equation , nonlinear system , inequality , mathematical analysis , partial differential equation , differential equation , physics , quantum mechanics
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.