Analysis & PDE

  • Anal. PDE
  • Volume 5, Number 2 (2012), 313-338.

Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Nalini Anantharaman and Gabriel Rivière

Full-text: Open access

Abstract

We study the time-dependent Schrödinger equation ıut=12Δu, on a compact Riemannian manifold on which the geodesic flow has the Anosov property. Using the notion of semiclassical measures, we prove various results related to the dispersive properties of the Schrödinger propagator, and to controllability.

Article information

Source
Anal. PDE, Volume 5, Number 2 (2012), 313-338.

Dates
Received: 28 July 2010
Revised: 27 August 2011
Accepted: 31 August 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731212

Digital Object Identifier
doi:10.2140/apde.2012.5.313

Mathematical Reviews number (MathSciNet)
MR2970709

Zentralblatt MATH identifier
1267.35176

Subjects
Primary: 35B37

Keywords
Schrödinger equation semiclassical analysis control theory

Citation

Anantharaman, Nalini; Rivière, Gabriel. Dispersion and controllability for the Schrödinger equation on negatively curved manifolds. Anal. PDE 5 (2012), no. 2, 313--338. doi:10.2140/apde.2012.5.313. https://projecteuclid.org/euclid.apde/1513731212


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