A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy
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Abstract:
In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form \begin{eqnarray*} u_{tt}-\Delta u+m^2u=f(u),& (t,x)\in [0,T)\times \mathbb {R}^n. \end{eqnarray*} Here $m\neq 0$ and the nonlinear power $f(u)$ satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in finite time.References
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Additional Information
- Yanjin Wang
- Affiliation: Graduate School of Mathematics, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
- Address at time of publication: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-15, Beijing, 100088, People’s Republic of China
- Email: wangyj@ms.u-tokyo.ac.jp, wang_jasonyj2002@yahoo.com
- Received by editor(s): November 10, 2006
- Received by editor(s) in revised form: November 23, 2006
- Published electronically: May 23, 2008
- Additional Notes: This work was supported by a Japanese government scholarship. The author wishes to express his deep gratitude to Professor Hitoshi Kitada for his constant encouragement and kind guidance. Thanks also go to the referees for their comments and careful reading of the manuscript
- Communicated by: Ronald A. Fintushel
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3477-3482
- MSC (2000): Primary 35L05, 35L15
- DOI: https://doi.org/10.1090/S0002-9939-08-09514-2
- MathSciNet review: 2415031