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A Note on a System of Cubic Nonlinear Klein–Gordon Equations in One Space Dimension

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Abstract

We study the Cauchy problem for a system of cubic nonlinear Klein–Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order \(O(t^{-1/2})\) in \(L^\infty \) as t tends to infinity without the condition of a compact support on the Cauchy data which was assumed in the previous works.

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Acknowledgments

The author would like to express his gratitude to Professor Hideaki Sunagawa for his comments at the beginning of this work. The author also thanks unknown referees for their useful comments.

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Correspondence to Donghyun Kim.

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Kim, D. A Note on a System of Cubic Nonlinear Klein–Gordon Equations in One Space Dimension. Differ Equ Dyn Syst 25, 431–451 (2017). https://doi.org/10.1007/s12591-015-0259-5

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  • DOI: https://doi.org/10.1007/s12591-015-0259-5

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