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Journal Articles Journal of Differential Equations Year : 2009

Exact boundary controllability of the nonlinear Schrödinger equation

Abstract

This paper studies the exact boundary controllability of the semilinear Schrödinger equation posed on a bounded domain Ω ⊂ Rn with either the Dirichlet boundary conditions or the Neumann boundary conditions. It is shown that if s > n/2, or 0 ≤ s < n/2 with 1 ≤ n < 2+2s, or s = 0,1 with n = 2, then the systems are locally exactly controllable in the classical Sobolev space Hs(Ω) around any smooth solution of the cubic Schrödinger equation.

Dates and versions

hal-00600680 , version 1 (15-06-2011)

Identifiers

Cite

Lionel Rosier, Bing-Yu Zhang. Exact boundary controllability of the nonlinear Schrödinger equation. Journal of Differential Equations, 2009, 246 (10), pp.4129-4153. ⟨10.1016/j.jde.2008.11.004⟩. ⟨hal-00600680⟩
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