Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance

Details Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance

2011-04-07

arxiv.org/abs/1104.1354v1

Mathematics

Analysis of PDEs

to appear in J. Differential Equations

Scientific paper

We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses satisfying the resonance relation. We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at the rate $O(|t|^{-1})$. In particular, our new condition includes the Yukawa type interaction, which has been excluded from the null condition in the sense of J.-M.Delort, D.Fang and R.Xue.

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