Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms

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概要

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• We consider the Cauchy problem for ∂t2u-∂x2u+u = -g(∂tu)3 on the real line. It is shown that if g>0, the solution has an additional logarithmic time decay in comparison with the free evolution in the sense of Lp, 2≤p≤∞. Moreover, the asymptotic profile of u(t,x) as t→+∞ 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.

• Mathematical Society of Japanの論文
• 2006-04-01

著者

• Sunagawa Hideaki

  Institute Of Mathematics University Of Tsukuba

関連論文

• Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms

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