Translator Disclaimer
July/August 2009 Exponential stability for the $2$-D defocusing Schrödinger equation with locally distributed damping
M. M. Cavalcanti, V. N. Domingos Cavalcanti, R. Fukuoka, F. Natali
Differential Integral Equations 22(7/8): 617-636 (July/August 2009).

Abstract

This paper is concerned with the study of the unique continuation property associated with the defocusing Schrödinger equation \begin{eqnarray*} iu_{t} +\Delta u - |u|^2u =0 ~\hbox{ in }\Omega \times (0,\infty), \end{eqnarray*} subject to Dirichlet boundary conditions, where $\Omega \subset \mathbb{R}^2$ is a bounded domain with smooth boundary $\partial \Omega=\Gamma$. In addition, we prove exponential decay rates of the energy for the damped problem \begin{eqnarray*} iu_{t} +\Delta u - |u|^2u +i a(x) u =0 \hbox{ in } \mathbb{R}^2 \times (0,\infty), \end{eqnarray*} provided that $a(x) \geq a_0 >0$ almost everywhere in $\Omega_{R}:=\{x\in \mathbb{R}^2 : |x| \geq R\}$, where $R>0$.

Citation

Download Citation

M. M. Cavalcanti. V. N. Domingos Cavalcanti. R. Fukuoka. F. Natali. "Exponential stability for the $2$-D defocusing Schrödinger equation with locally distributed damping." Differential Integral Equations 22 (7/8) 617 - 636, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35509
MathSciNet: MR2532114

Subjects:
Primary: 35Q55
Secondary: 35B35, 35B40, 35B60

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.22 • No. 7/8 • July/August 2009
Back to Top