EXPONENTIAL DECAY FOR A CLASS OF NON-LOCAL NON-LINEAR SCHR O?DINGER EQUATIONS WITH LOCALISED DAMPING

被引：0
|
作者：
DE Leo, M. A. R. I. A. N. O. [1 ]
机构：
[1] Univ Nacl Sur, Dept Matemat, Inst Matemat Bahia Blanca INMABB CONICET, Av Alem 1253, RA-8000 Bahia Blanca, Buenos Aires, Argentina
来源：
COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2022年 / 20卷 / 06期
关键词：
Stabilisation; localised damping; nonlinear Schro?dinger; Hartree potential; SCHRODINGER-EQUATION; CONTROLLABILITY; STABILIZATION;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the exponential decay of both the charge and the free energy for solutions of a family of non-linear, non-local Schro & BULL;dinger equations with localised damping on the whole line. We first establish an observability inequality for the linear flow, from which we obtain the result in the linear case. Then we consider the non-linear case and by perturbative arguments we obtain the exponential decay for solutions with small initial data. Finally we discuss qualitative aspects of the dynamics and show that the stabilisation rate becomes smaller as the free damping region is chosen around the origin.
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收藏
页码：1685 / 1701
页数：17
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