Differential and Integral Equations

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

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