论文标题
一维非线性波方程的渐近能分布
Asymptotic energy distribution of one-dimensional nonlinear wave equation
论文作者
论文摘要
在这项工作中，我们考虑在一维空间中散发非线性波方程。我们表明，几乎所有能量都位于光锥$ | x | = | t | $附近，因为时间趋于无限。我们还证明，任何光锥最终都将包含一些能量。作为应用程序，我们获得了解决方案的渐近行为，以使用紧凑的初始数据聚焦一维波方程。
In this work we consider the defocusing nonlinear wave equation in one-dimensional space. We show that almost all energy is located near the light cone $|x|=|t|$ as time tends to infinity. We also prove that any light cone will eventually contain some energy. As an application we obtain a result about the asymptotic behaviour of solutions to focusing one-dimensional wave equation with compact-supported initial data.
