Analysis and Numerics of Evolution Equations
The dynamics of many systems in nature, science, and technology reflect their laws mathematically as evolution equations. The center is devoted to the theoretical and numerical analysis of evolution equations that describe processes of transport and transformation of material continua. Investigation of similar issues has since long been the central theme pursued by the consistently developed Schwerpunkt Analysis und Numerik at the Department of Mathematics and Statistics at the University of Konstanz. With a decided emphasis on interdisciplinary aspects, the center is conceived to focus and bundle ressources and efforts distinctly further.
- FB Mathematik und Statistik
|(2013): Boundary Layers for Quantum Semiconductor Models|
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.
|Laufzeit:||01.12.2009 – 31.10.2012|