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March 2007 Optimal Control of the Stationary Quantum Drift-Diffusion Model
A. Unterreiter, S. Volkwein
Commun. Math. Sci. 5(1): 85-111 (March 2007).


In this work an optimal control problem for a stationary quantum drift diffusion (QDD) model is analyzed. This QDD model contains four space-dependent observables: The non-negative particle density of electrons, the electrostatic potential, the quantum quasi-Fermi potential and the current density. The goal is to optimize the shape of quantum barriers in a quantum diode. Existence of optimal solutions is proved. Moreover, first-order necessary optimality conditions are derived.


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A. Unterreiter. S. Volkwein. "Optimal Control of the Stationary Quantum Drift-Diffusion Model." Commun. Math. Sci. 5 (1) 85 - 111, March 2007.


Published: March 2007
First available in Project Euclid: 5 April 2007

MathSciNet: MR2310635

Primary: 35J55 , 49J20 , 49K20

Keywords: optimal control , optimality conditions , quantum drift diffusion model

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 1 • March 2007
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