International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 471-483
doi:10.1155/S0161171286000601

Decay of solutions of a system of nonlinear Klein-Gordon equations

José Ferreira1 and Gustavo Perla Menzala1,2

1Institute of Mathematics, UFRJ P.O. Box 68530, Rio de Janeiro, RJ, Brazil
2National Laboratory for Scientific Computation, LNCC/CNPq, Lauro Muller 455 22290, Botafogo, Rio de Janeiro, RJ, Brazil

Received 20 November 1985

Copyright © 1986 José Ferreira and Gustavo Perla Menzala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein-Gordon equations. We have two basic results: First, in the L∞(ℝ3) norm, solutions decay like 0(t−3/2) as t→+∞ provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm as t→+∞.