Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model

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2012
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Bian, Shen
Chen, Li
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Journal of Differential Equations. 2012, 253(1), pp. 356-377. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2012.03.008
Zusammenfassung

We study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift–diffusion model of a semiconductor. We prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions. We prove analytical estimates of the remainder terms of this asymptotic expansion, and confirm by means of numerical simulations that these remainder estimates are sharp.

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Fachgebiet (DDC)
510 Mathematik
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Quantum drift–diffusion model, Boundary layer, Elliptic system, Variational methods
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ISO 690BIAN, Shen, Li CHEN, Michael DREHER, 2012. Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model. In: Journal of Differential Equations. 2012, 253(1), pp. 356-377. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2012.03.008
BibTex
@article{Bian2012Bound-22045,
  year={2012},
  doi={10.1016/j.jde.2012.03.008},
  title={Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model},
  number={1},
  volume={253},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={356--377},
  author={Bian, Shen and Chen, Li and Dreher, Michael}
}
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