Communications in Mathematical Sciences

Optimal Control of the Stationary Quantum Drift-Diffusion Model

A. Unterreiter and S. Volkwein

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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.

Article information

Commun. Math. Sci., Volume 5, Issue 1 (2007), 85-111.

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Primary: 35J55 49J20: Optimal control problems involving partial differential equations 49K20: Problems involving partial differential equations

Optimal control quantum drift diffusion model optimality conditions


Unterreiter, A.; Volkwein, S. Optimal Control of the Stationary Quantum Drift-Diffusion Model. Commun. Math. Sci. 5 (2007), no. 1, 85--111.

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