Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations. (10th November 2015)

• Record Type: Journal Article
• Authors: Kutev, Nikolay; Kolkovska, Natalia; Dimova, Milena
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2287
• Page End: 2297
• Publication Date: 2015-11-10
• Subjects: finite time blow up, Klein–Gordon equation -- generalized Boussinesq equation -- arbitrary high positive energy -- ssubclass 35L70 -- 35L75 -- 35B44; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3639
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.