| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2023-0401 |
| Long time behaviour of the solutions of nonlinear wave equation |
| Jianjun Liu,duohui xiang |
| Keywords:long time behaviour, nonlinear wave equation, Birkhoff normal form |
| 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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