A Large Data Regime for non-linear Wave Equations
A Large Data Regime for non-linear Wave Equations
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DOI：
10.4171/jems/597
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发表时间：
2012-10
影响因子：
2.6
通讯作者：
Jinhua Wang;P. Yu
中科院分区：
文献类型：
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作者：
Jinhua Wang;P. Yu
对于R上具有零形式非线性项的半线性波动方程，我们给出了一个开放的初始数据集，该初始数据集在能量空间中允许很大，但我们仍然可以得到整体解.我们还展示了一组本地化的数据，相应的解决方案是强烈集中，这在几何术语意味着波传播沿着一个特定的传入零测地线在这样一种方式，几乎所有的能量被限制在一个管状邻域的测地线，几乎没有能量辐射出这个管状邻域。
For semi-linear wave equations with null form non-linearities on R, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also exhibit a set of localized data for which the corresponding solutions are strongly focused, which in geometric terms means that a wave travels along an specific incoming null geodesic in such a way that almost all of the energy is confined in a tubular neighborhood of the geodesic and almost no energy radiating out of this tubular neighborhood.