Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

Date

2018-03-14

Authors

Dimova, Milena
Kolkovska, Natalia
Kutev, Nikolai

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

Description

Keywords

Finite time blow up, Concavity method, Klein-Gordon equation, Double dispersive equation

Citation

Dimova, M., Kolkovska, N., & Kutev, N. (2018). Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems. <i>Electronic Journal of Differential Equations, 2018</i>(68), pp. 1-16.

Rights

Attribution 4.0 International

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