Viscous quantum hydrodynamics and parameter-elliptic systems

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2011
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Mathematical Methods in the Applied Sciences. 2011, 34(5), pp. 520-531. ISSN 0170-4214. Available under: doi: 10.1002/mma.1377
Zusammenfassung

The viscous quantum hydrodynamic model derived for semiconductor simulation is studied in this paper. The principal part of the vQHD system constitutes a parameter-elliptic operator provided that boundary conditions satisfying the Shapiro–Lopatinskii criterion are specified. We classify admissible boundary conditions and show that this principal part generates an analytic semigroup, from which we then obtain the local in time well-posedness. Furthermore, the exponential stability of zero current and large current steady states is proved, without any kind of subsonic condition. The decay rate is given explicitly.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Semiconductor model, boundary conditions, analytic semigroup, exponential stability, decay rate
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ISO 690CHEN, Li, Michael DREHER, 2011. Viscous quantum hydrodynamics and parameter-elliptic systems. In: Mathematical Methods in the Applied Sciences. 2011, 34(5), pp. 520-531. ISSN 0170-4214. Available under: doi: 10.1002/mma.1377
BibTex
@article{Chen2011Visco-19145,
  year={2011},
  doi={10.1002/mma.1377},
  title={Viscous quantum hydrodynamics and parameter-elliptic systems},
  number={5},
  volume={34},
  issn={0170-4214},
  journal={Mathematical Methods in the Applied Sciences},
  pages={520--531},
  author={Chen, Li and Dreher, Michael}
}
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