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The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential

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2015

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https://doi.org/10.1016/j.jmaa.2015.01.019
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Journal of Mathematical Analysis and Applications. 2015, 425(2), pp. 1113-1133. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2015.01.019

Zusammenfassung

We investigate the viscous model of quantum hydrodynamics, which describes the charge transport in a certain semiconductor. Quantum mechanical effects lead to third order derivatives, turning the stationary system into an elliptic system of mixed order in the sense of Douglis–Nirenberg. In the case most relevant to applications, the semiconductor device features a piecewise constant barrier potential. In the case of thermodynamic equilibrium, we obtain asymptotic expansions of interfacial layers of the particle density in neighbourhoods of the jump points of this barrier potential, and we present rigorous proofs of uniform estimates of the remainder terms in these asymptotic expansions.

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Fachgebiet (DDC)
510 Mathematik

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Boundary layers, Quantum hydrodynamics, Remainder estimates

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ISO 690DREHER, Michael, Johannes SCHNUR, 2015. The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential. In: Journal of Mathematical Analysis and Applications. 2015, 425(2), pp. 1113-1133. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2015.01.019
BibTex
@article{Dreher2015-05combi-39754,
  year={2015},
  doi={10.1016/j.jmaa.2015.01.019},
  title={The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential},
  number={2},
  volume={425},
  issn={0022-247X},
  journal={Journal of Mathematical Analysis and Applications},
  pages={1113--1133},
  author={Dreher, Michael and Schnur, Johannes}
}
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