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

Roberto Triggiani ()
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Roberto Triggiani: University of Virginia, Department of Mathematics

A chapter in Functional Analysis and Evolution Equations, 2007, pp 613-636 from Springer

Abstract: 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.

Keywords: Exact controllability; Schrödinger equation; Riemannian manifold (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_37

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DOI: 10.1007/978-3-7643-7794-6_37

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