Local energy decay for scalar fields on time dependent non-trapping backgrounds
Local energy decay for scalar fields on time dependent non-trapping backgrounds
复制标题
时间相关非捕获背景上标量场的局部能量衰减
DOI：
10.1353/ajm.2020.0019
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
D. Tataru
中科院分区：
文献类型：
--
作者：
Jason Metcalfe;Jacob Sterbenz;D. Tataru
研究了非俘获渐近平坦时空上标量波动方程解的局部能量衰减估计。我们的目标是双重的。首先，我们考虑平稳情况，在这种情况下，我们可以提供局部能量衰减界的全谱表征；这种性质在平稳对称情况下得到简化。然后我们考虑几乎平稳，几乎对称的情况。在那里我们建立了两个主要的结果：第一个是“两点”局部能量衰减估计，这是有效的一般类（非对称）几乎平稳波方程，满足一定的非共振性质在零频率。第二个结果也需要几乎对称的条件，即通过有限维时间相关的稳定和不稳定子空间在能量空间中建立指数三分法，并通过通常的局部能量衰减估计在无限维补上分散解。
abstract:We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a ``two point'' local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a certain nonresonance property at zero frequency. The second result, which also requires the almost symmetry condition, is to establish an exponential trichotomy in the energy space via finite dimensional time dependent stable and unstable sub-spaces, with an infinite dimensional complement on which solutions disperse via the usual local energy decay estimate.
Pontryagin空间中KleinâGordon方程的谱论
影响因子：
2.4
作者：
Langer;Najman;Tretter
通讯作者：
Tretter