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

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→+∞.