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  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.
Differential and Integral Equations
Lasiecka, I., Triggiani, R., & Da Prato, G. (1992). Optimal regularity, exact controllability and uniform stabilization of schrodinger equations with dirichlet control. Differential and Integral Equations, 5 (3), 521-535. Retrieved from https://digitalcommons.memphis.edu/facpubs/5410