Abstract We prove a Nekhoroshev type theorem for the nonlinear wave equation (NLW) (0.1) u t t = u x x − m u − f ( u ) under Dirichlet boundary conditions where f is an analytic function. More precisely, we prove the subexponential long time stability result of the origin for equation (0.1) by using Birkhoff normal form technique for infinite dimensional Hamiltonian systems and the so-called tame property of the nonlinearity in Gevrey (or analytic) space, which is inspired by the work [6] where the authors proved the polynomial long time stability result in Sobolev space for a class of Hamiltonian PDEs.

中文翻译：

---

非线性波动方程的 Nekhoroshev 型定理

摘要 我们证明了狄利克雷边界条件下非线性波动方程 (NLW) (0.1) utt = uxx − mu − f ( u ) 的涅霍罗舍夫型定理，其中 f 是解析函数。更准确地说，我们通过使用无限维哈密顿系统的 Birkhoff 范式技术和 Gevrey（或解析）空间中非线性的所谓驯服性质，证明了方程 (0.1) 原点的次指数长时间稳定性结果，即受到工作 [6] 的启发，作者证明了 Sobolev 空间中一类哈密顿偏微分方程的多项式长时间稳定性结果。