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Exact Controllability in L 2(Ω) of the Schrödinger Equation in a Riemannian Manifold with L 2(Σ1)-Neumann Boundary Control

In: Functional Analysis and Evolution Equations

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  • Roberto Triggiani

    (University of Virginia, Department of Mathematics)

Abstract

We consider the Schrödinger equation, with H 1-level terms having variable coefficients in time and space, as defined on an open bounded connected set Ω of an n-dimensional complete Riemannian manifold. We show that it is exactly controllable on the state space L 2(Ω) on an arbitrarily small interval [0, T], by means of Neumann boundary controls in the class L 2(0, T;L 2(Г1)), where Г1 = ∂Ω SHIELA Г0, and the equation is homogeneous on Г0, either in the Dirichlet or in the Neumann B.C. Different geometric conditions apply in the two cases. This result is a vast generalization over the literature.

Suggested Citation

  • Roberto Triggiani, 2007. "Exact Controllability in L 2(Ω) of the Schrödinger Equation in a Riemannian Manifold with L 2(Σ1)-Neumann Boundary Control," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 613-636, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_37
    DOI: 10.1007/978-3-7643-7794-6_37
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