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

2014/06/30 by Donghyun Kim
Mathematics · #math.AP #msc:35L70 #msc:35B40 #msc:35L15

paper · pdf · doi:10.1142/s0219891615500216

published as 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

arxiv created 2014/08/01 · arxiv updated 2016/02/11

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∈[2,∞] as t tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

Citations

• Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities
• Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance