On compressible Navier-Stokes system with non-zero inflow/outflow boundary conditions
Abstract:
We discuss the existence of weak solutions to the compressible evolutionary Navier-Stokes system with non-zero inflow/ouflow boundary conditions. The hard sphere pressure-density state equation is used to provide the necessary a priori bounds.
08.08.17 09:00
Ansgar Jüngel
(TU Wien)
Nano processors: unimaginably small and unbelievably fast. Model hierarchy, analysis, simulations
Abstract:
The success of computer technology is mainly based on the miniaturization of the semiconductor devices in computer processors. As actual devices have a size of a few nanometers only, this process seems to reach its physical limit, and new technologies or materials are needed. In this talk, some aspects of the mathematical modeling of semiconductor devices, the analysis of the resulting nonlinear partial differential equations, and their numerical simulation will be presented. We focus on kinetic equations and their diffusion moment models, mixed finite-element and finite-volume approximations. In the analytical part, we detail a new technique, applied to a quantum diffusion equation. The new technique uses systematic integration by parts, which is based on a polynomial decision problem arising in real algebraic geometry and which allows for the derivation of a priori estimates.
13.06.17 09:00
prof. RNDr. Eduard Feireisl, DrSc.
árka Nečasová, Milan Pokorný
chairmen