| Speaker: | Irene M. Gamba, University of Texas at Austin |
| Title: | Quantum trajectory models and the boundary value problem |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
We look at quantum trajectory (hydrodynamic) models (QHM)-Poisson systems in bounded domains with inflow boundary conditions in the context of charged transport induced by an electric field induced by long range interactions for a rather general thermalization closure. These problems of dispersive Hamilton Jacobi type appear in the modeling of nano-scale electronic devices as well as Bose Einstein condensates and other approximations to charged non-linear Shroedinger transport subject to open boundary conditions by WKB expansions. We show non-existence of weak solutions to stationary states for a large set of boundary conditions, and, in particular, a blow up in finite time for transient solutions. However the stationary problem is solvable when a nonlinear viscous-friction term is present. In the transient case, we show blow up in finite time for large energy initial data. This work is a result of a series of collaborations with A. Juengel and P. Zhang.
Last revised: 02/22/06 By: sgkim@math.tamu.edu