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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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http://nbn-resolving.de/urn:nbn:de:bsz:352-220459
DOI (zitierfähiger Link)
https://doi.org/10.1016/j.jde.2012.03.008
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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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

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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