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- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity; Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-011-9662-2
- Publisher site
- See Article on Publisher Site
Abstract
This article studies the Cauchy problem for the coupled nonlinear Klein-Gordon equations with damping terms. By introducing a family of potential wells, we derive the invariant sets and the vacuum isolating of solutions. Furthermore, we show the global existence, finite time blow-up, as well as the asymptotic behavior of solutions. In particular, we establish a sharp criterion for global existence and blow-up of solutions when E(0)<d. Finally, a blow-up result of solutions with E(0)=d is also proved.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 17, 2011