Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities

Donghyun Kim; Hideaki Sunagawa

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arXiv · 1307.7890

Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities

Donghyun Kim·Hideaki Sunagawa

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Abstract

We consider the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional logarithmic decay in comparison with the free evolution in the sense of $L^p$, $2\le p \le \infty$.

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Donghyun Kim, Hideaki Sunagawa. 2013-07-30. Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities. https://arxiv.org/abs/1307.7890

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