Communications in Mathematical Sciences

Volume 5 (2007)

Number 1

Optimal Control of the Stationary Quantum Drift-Diffusion Model

Pages: 85 – 111



A. Unterreiter

S. Volkwein


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.


Optimal control; quantum drift diffusion model; optimality conditions

2010 Mathematics Subject Classification

49J20, 49K20

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