Local exact bilinear control of the Schrödinger equation∗
Laboratoire de Mathématiques de Versailles, Université de Versailles St Quentin, 78035 Versailles cedex, France.
Received: 6 June 2016
Accepted: 7 June 2016
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 Γ0 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 Γ0 and the linear controllability results with real and sufficiently regular controls.
Mathematics Subject Classification: 35B65 / 35Q41
Key words: Schrödinger equation / bilinear control
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