Regularity of the attractor for a weakly damped nonlinear Schrodinger equation on R

被引：18

作者：

Akroune, N ^{[1
]}

机构：

[1] Univ Cergy Pontoise, F-95302 Cergy, Pontoise, France

来源：

APPLIED MATHEMATICS LETTERS | 1999年 / 12卷 / 03期

关键词：

nonlinear Schrodinger equations; weak damping; global attractor;

D O I：

10.1016/S0893-9659(98)00170-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long time behaviour of the solutions to a nonlinear Schrodinger equation, in presence of a damping term, and a forcing term, when the space variable x varies over R. We show that the long time behaviour is described by an attractor which captures all the trajectories in H-1(R). Our main result is concerned with the asymptotic smoothing effect for the equations. In other words, we prove that the attractor is included and compact in H-2(R), generalizing results proven in [1] in the compact (bounded) case (see also [2]). (C) 1999 Elsevier Science Ltd. All rights reserved.

引用

页码：45 / 48

页数：4