Differential and Integral Equations

Exponential stability for the defocusing semilinear Schrödinger equation with locally distributed damping on a bounded domain

César Augusto Bortot and Wellington José Corrêa

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Abstract

In this paper, we study the exponential stability for the semilinear defocusing Schrödinger equation with locally distributed damping on a bounded domain $\Omega \subset \mathbb{R}^n$ with smooth boundary $\partial \Omega$. The proofs are based on a result of unique continuation property due to Cavalcanti et al. [15] and on a forced smoothing effect due to Aloui [2] combined with ideas from Cavalcanti et. al. [15], [16] adapted to the present context.

Article information

Source
Differential Integral Equations Volume 31, Number 3/4 (2018), 273-300.

Dates
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1513652427

Subjects
Primary: 35B35: Stability 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Bortot, César Augusto; Corrêa, Wellington José. Exponential stability for the defocusing semilinear Schrödinger equation with locally distributed damping on a bounded domain. Differential Integral Equations 31 (2018), no. 3/4, 273--300. https://projecteuclid.org/euclid.die/1513652427


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