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Stabilization and Control for the Nonlinear Schrödinger Equation on a Compact Surface

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Abstract

In this paper, we study the stabilization property and the exact controllability for the nonlinear Schrödinger equation on a two dimensional compact Riemannian manifold, without boundary. We use a pseudo-differential dissipation. The proofs are based on a result of propagation of singularities and on recent dispersion estimates (Strichartz type inequalities) due to N. Burq, P. Gérard and N. Tzvetkov.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences de Tunis et LAMSIN, 1060, Tunis, Tunisia

    B. Dehman

  2. Université de Paris-Sud, Bâtiment 425, 91405, Orsay, France

    P. Gérard

  3. Laboratoire Jean-Alexandre Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, 06108, Nice cedex 2, France

    G. Lebeau

Authors
  1. B. Dehman
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  2. P. Gérard
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  3. G. Lebeau
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Correspondence to B. Dehman.

Additional information

B. Dehman is supported by the Tunisian Ministry for Scientific Research and Technology (MRST), within the LAB-STI-02 program

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Dehman, B., Gérard, P. & Lebeau, G. Stabilization and Control for the Nonlinear Schrödinger Equation on a Compact Surface. Math. Z. 254, 729–749 (2006). https://doi.org/10.1007/s00209-006-0005-3

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  • DOI: https://doi.org/10.1007/s00209-006-0005-3

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