Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 4
227
Views
13
CrossRef citations to date
0
Altmetric
Articles

Sign-preserving functionals and blow-up to Klein–Gordon equation with arbitrary high energy

, &
Pages 860-873 | Received 13 Nov 2014, Accepted 06 Apr 2015, Published online: 08 May 2015
 

Abstract

The global behaviour of the weak solutions of the Cauchy problem to nonlinear Klein–Gordon equation with combined power-type nonlinearity is studied. Finite time blow-up of the solutions with arbitrary high positive initial energy is proved under general structural conditions on the initial data. A new functional, invariant under the flow of the equation, is introduced and investigated.

AMS Subject Classifications:

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Bulgarian Science Fund under grant DFNI I-02/9.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.