论文标题
耗散非线性schrödinger方程的渐近行为
Asymptotic behavior for a dissipative nonlinear Schrödinger equation
论文作者
论文摘要
我们考虑具有非线性耗散的schrödinger方程\ begin {equation*} i \ partial _t u +Δu=λ|假设$ \ frac {2} {n+2} <α<\ frac2n $，我们对解决方案的长期行为进行精确描述（包括$ l^2 $和$ l^\ infty $和$ l^\ infty $，以及非属性的衰减率），则用于一类任意大型初始数据的类别。
We consider the Schrödinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +Δu=λ|u|^αu \end{equation*} in ${\mathbb R}^N $, $N\geq1$, where $λ\in {\mathbb C} $ with $\Imλ<0$. Assuming $\frac {2} {N+2}<α<\frac2N$, we give a precise description of the long-time behavior of the solutions (including decay rates in $L^2$ and $L^\infty $, and asymptotic profile), for a class of arbitrarily large initial data.
