数学
独特性
波动方程
背景(考古学)
数学分析
领域(数学分析)
数学证明
边值问题
理论(学习稳定性)
边界(拓扑)
指数函数
薛定谔方程
几何学
古生物学
机器学习
计算机科学
生物
作者
Marcelo M. Cavalcanti,Wellington José Corrêa,V. N. Domingos Cavalcanti
摘要
We are concerned with the existence as well as the exponential stability in H1-level for the damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω with smooth boundary ∂Ω. The proofs of the existence are based on the properties of pseudo-differential operators introduced in Dehman et al. [Math. Z. 254, 729–749 (2006)] and a Strichartz estimate proved by Anton [Bull. Soc. Math. Fr. 136, 27–65 (2008)], while the exponential stability is achieved by combining arguments firstly considered by Zuazua [J. Math. Pures Appl. 9, 513–529 (1991)] for the wave equation adapted to the present context and a global uniqueness theorem. In addition, we proved propagation results for the linear Schrödinger equation for any dimensional and for any (reasonable) boundary conditions employing microlocal analysis.
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