Strong instability of standing waves for nonlinear Klein-Gordon equations

Pages: 315 - 322, Volume 12, Issue 2, February 2005

doi:10.3934/dcds.2005.12.315       Abstract        Full Text (194.6K)       Related Articles

Masahito Ohta - Department of Mathematics, Faculty of Science, Saitama University, Japan (email)
Grozdena Todorova - Department of Mathematics, University of Tennessee, Knoxville, TN 37096-1300, United States (email)

Abstract: The strong instability of ground state standing wave solutions $e^{i\omega t}\phi_{\omega}(x)$ for nonlinear Klein-Gordon equations has been known only for the case $\omega=0$. In this paper we prove the strong instability for small frequency $\omega$.

Keywords:  Stability/instability problems, ground state standing waves, blow-up, nonlinear Klein-Gordon equation.
Mathematics Subject Classification:  35L70, 35B35, 35A15.

Received: July 2003;      Revised: June 2004;      Published: December 2004.