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2017 Local energy decay and smoothing effect for the damped Schrödinger equation
Moez Khenissi, Julien Royer
Anal. PDE 10(6): 1285-1315 (2017). DOI: 10.2140/apde.2017.10.1285

Abstract

We prove the local energy decay and the global smoothing effect for the damped Schrödinger equation on d . The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation that we consider.

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Moez Khenissi. Julien Royer. "Local energy decay and smoothing effect for the damped Schrödinger equation." Anal. PDE 10 (6) 1285 - 1315, 2017. https://doi.org/10.2140/apde.2017.10.1285

Information

Received: 3 June 2015; Revised: 14 March 2017; Accepted: 24 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1372.35262
MathSciNet: MR3678489
Digital Object Identifier: 10.2140/apde.2017.10.1285

Subjects:
Primary: 35B40 , 35B65 , 35Q41 , 47A55 , 47B44

Keywords: damped Schrödinger equation , local energy decay , resolvent estimates , Smoothing effect

Rights: Copyright © 2017 Mathematical Sciences Publishers

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