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# Global existence of small amplitude solutions to one-dimensional nonlinear Klein-Gordon systems with different masses

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### Abstract

We study the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate $$O(t^{-(1/2-1/p)})$$ in $$L^p$$, $$p\in[2,\infty]$$ as $$t$$ tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

### Author and article information

###### Journal
2014-06-16
2014-08-01
1406.3947
10.1142/S0219891615500216

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

###### Custom metadata
35L70, 35B40, 35L15
J. Hyper. Differential Equations 12 (2015), 745-762
17 pages arXiv admin note: text overlap with arXiv:1307.7890; and text overlap with arXiv:1104.1354 by other authors
math.AP

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