Strong instability of standing waves for nonlinear Klein-Gordon equations

Masahito Ohta; Grozdena Todorova

doi:10.3934/dcds.2005.12.315

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2005, Volume 12, Issue 2: 315-322. Doi: 10.3934/dcds.2005.12.315

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Strong instability of standing waves for nonlinear Klein-Gordon equations

Masahito Ohta^1, and
Grozdena Todorova^2,

1.
Department of Mathematics, Faculty of Science, Saitama University
2.
Department of Mathematics, University of Tennessee, Knoxville, TN 37096-1300

Received: June 30, 2003

Revised: May 31, 2004

Published: January 2005

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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 $\omega$.

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Mathematics Subject Classification: 35L70, 35B35, 35A15.

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