Long time behaviour of the solutions of nonlinear wave equation |
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| Institution: | College of Mathematics, Sichuan University, Chengdu 610065, China,College of Mathematics, Sichuan University, Chengdu 610065, China |
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| Abstract: | In this paper, we consider the nonlinear wave equation
$$u_{tt}-\Delta u+mu+f(x,u)=0,\ x\in\mb{T}^{d}:=(\mb{R}/2\pi\mb{Z})^{d},$$
where $m>0$ and $f$ is an analytic function of order at least two in $u$. The long time behaviour of its solutions is proved by Birkhoff normal form. |
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| Keywords: | long time behaviour nonlinear wave equation Birkhoff normal form |
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