Milena Dimova, Natalia Kolkovska, Nikolai Kutev
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.
Submitted August 2, 2017. Published March 14, 2018.
Math Subject Classifications: 35B44, 34A40, 35A24, 35L75.
Key Words: Finite time blow up; concavity method; Klein-Gordon equation;
double dispersive equation.
Show me the PDF file (356 KB), TEX file for this article.
 |
Milena Dimova University of National and World Economy Students' Town, 1700 Sofia, Bulgaria email: mdimova@unwe.bg |
|---|---|
 |
Natalia Kolkovska Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria email: natali@math.bas.bg |
 |
Nikolai Kutev Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria email: kutev@math.bas.bg |
Return to the EJDE web page