Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 58, Number 2 (2006), 379-400.
Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms
We consider the Cauchy problem for on the real line. It is shown that if , the solution has an additional logarithmic time decay in comparison with the free evolution in the sense of , . Moreover, the asymptotic profile of as is obtained. We also discuss a generalization. Consequently we see that the "null condition" in the sense of J.-M. Delort (Ann. Sci. École Norm. Sup., 34 (2001), 1--61) is not optimal for small data global existence for nonlinear Klein-Gordon equations.
J. Math. Soc. Japan, Volume 58, Number 2 (2006), 379-400.
First available in Project Euclid: 1 June 2006
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SUNAGAWA, Hideaki. Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms. J. Math. Soc. Japan 58 (2006), no. 2, 379--400. doi:10.2969/jmsj/1149166781. https://projecteuclid.org/euclid.jmsj/1149166781