论文标题
在整个空间中湿的非线性schr {Ö} dinger方程的有限时间灭绝
Finite time extinction for a damped nonlinear Schr{ö}dinger equation in the whole space
论文作者
论文摘要
我们考虑在整个空间中设置的非线性schr {Ö} dinger方程，具有单一的交互和外部源。我们首先建立解决方案的存在和独特性，然后在低空间维度上显示解决方案在有限的时间消失。在初始数据的小假设和外部源上的一些合适的其他假设下，我们还表明我们可以选择上限溶液消失的上限。
We consider a nonlinear Schr{ö}dinger equation set in the whole space with a single power of interaction and an external source. We first establish existence and uniqueness of the solutions and then show, in low space dimension, that the solutions vanish at a finite time. Under a smallness hypothesis of the initial data and some suitable additional assumptions on the external source, we also show that we can choose the upper bound on which time the solutions vanish.
