Geodesic
Local exact bilinear control of the Schrödinger equation
Puel, Jean-Pierre1 
1 Laboratoire de Mathématiques de Versailles, Université de Versailles St Quentin, 78035 Versailles cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1264-1281

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We are going to prove the local exact bilinear controllability for a Schrödinger equation, set in a bounded regular domain, in a neighborhood of an eigenfunction corresponding to a simple eigenvalue in dimension N≤3. For a general domain we will require a non degeneracy condition of the normal derivative of the eigenfunction on a part Γ 0 of the boundary satisfying the Geometric Control Condition (see [G. Lebeau. J. Math. Pures Appl. 71 (1992) 267–291]) and for a rectangle when N=2 or an interval for N=1 no further condition. In the general case we will use real potentials concentrated in the neighborhood of Γ 0 and the linear controllability results with real and sufficiently regular controls.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016049
Classification : 35B65, 35Q41
Keywords: Schrödinger equation, bilinear control

Puel, Jean-Pierre 1

1 Laboratoire de Mathématiques de Versailles, Université de Versailles St Quentin, 78035 Versailles cedex, France. 
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     title = {Local exact bilinear control of the {Schr\"odinger} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1264--1281},
     publisher = {EDP-Sciences},
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Puel, Jean-Pierre. Local exact bilinear control of the Schrödinger equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1264-1281. doi: 10.1051/cocv/2016049

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