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

2011/04/07 by Yuichiro Kawahara, Kawahara, Yuichiro, Hideaki Sunagawa +1 · 1 citation
Mathematics · #35B40 #35L15 #35L70 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35L15 #msc:35L70

paper · pdf · doi:10.48550/arxiv.1104.1354

to appear in J. Differential Equations

arxiv created 2011/04/07 · arxiv updated 2011/04/08

Abstract

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

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