Optimal regularity, exact controllability and uniform stabilization of schrodinger equations with dirichlet control


We first identify the space of optimal regularity of a Schrödinger equation defined on a smooth bounded domain Ω ⊂ Rn with L2(0, T; L2(λ)) -nonhomogeneous term (control) in the Dirichlet boundary conditions. Next, we prove exact controllability and uniform stabilization results on this optimal space, the latter via an explicit dissipative feedback operator. As a consequence of these results, the abstract theory of the optimal quadratic cost problem over an infinite horizon and related Algebraic Riccati Equation as in [3] is applicable to this Schrodinger mixed problem. This, in particular, provides another stabilizing feedback operator, generally non-dissipative, defined in terms of the corresponding Riccati operator. © 1992, Khayyam Publishing. All rights reserved.

Publication Title

Differential and Integral Equations

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