Abstract
We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂) 2 t - ∂ 2 x + m 2 j ))uJ = N j (∂u). j = 1,..., I. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.
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