We study the global existence of solutions to semilinear damped wave equations in the scattering case with power-type nonlinearity on the derivatives, posed on nontrapping asymptotically Euclidean manifolds. The main idea is to shift initial time by local existence. As a result, we could convert the damping term to small enough perturbation and obtain the global existence.

中文翻译：

---

散射情况下半线性阻尼波方程的整体存在

我们研究了在导数上具有幂型非线性的散射情况下的半线性阻尼波方程解的整体存在性，这些条件存在于非陷波渐近欧氏流形上。主要思想是通过本地存在来转移初始时间。结果，我们可以将阻尼项转换为足够小的扰动并获得整体存在。