Analysis and Numerics of Evolution Equations with Applications in the Science

Institutions
  • Department of Mathematics and Statistics
Publications
  Schnur, Johannes (2013): Boundary Layers for Quantum Semiconductor Models

Boundary Layers for Quantum Semiconductor Models

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In the present thesis, we consider variants of the stationary one-dimensional quantum drift-diffusion model and the stationary one-dimensional viscous quantum hydrodynamic model with a non-smooth barrier potential. For the latter, existence results are established by a reformulation in terms of a viscosity-adjusted Fermi-level, variational methods and fixed point arguments. The dependence of solutions on the quantum and viscous parameters is examined and the combined viscous semi-classical limit is considered. The existence of fluid-dynamical boundary layers is verified by the construction of asymptotic expansions of the solutions.

Origin (projects)

Funding sources
Name Finanzierungstyp Kategorie Project no.
third-party funds research funding program 792/09
Further information
Period: 01.12.2009 – 31.10.2012