Well-posedness and energy decay estimates in the Cauchy problem for the damped defocusing Schrödinger equation

https://doi.org/10.1016/j.jde.2016.11.002Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, we study the existence at the H1-level as well as the stability for the damped defocusing Schrödinger equation in Rd. The considered damping coefficient is time-dependent and may vanish at infinity. To prove the existence, we employ the method devised by Özsarı, Kalantarov and Lasiecka [27], which is based on monotone operators theory. In particular, when d=1 or d=2, we obtain the uniqueness. Decay estimates for the L2-level and (H1Lp+2)-level energies are established with the help of direct multipliers method, coupled with refined energy estimates and a lower semi-continuity argument.

Cited by (0)

1

Research of Marcelo M. Cavalcanti partially supported by the CNPq Grant 300631/2003-0.

2

Research of Valéria N. Domingos Cavalcanti partially supported by the CNPq Grant 304895/2003-2.