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

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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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510 Mathematik
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partial differential equations
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ISO 690DREHER, Michael, Johannes SCHNUR, 2014. The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential
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@techreport{Dreher2014combi-27502,
  year={2014},
  series={Konstanzer Schriften in Mathematik},
  title={The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential},
  number={329},
  author={Dreher, Michael and Schnur, Johannes}
}
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