Spring 1998

      Analysis to Models of Charged Transport

M393C -- CAM393C unique number 52370 MW 2:30 - 4:30

                  Prof. Irene M. Gamba

                      Description

Kinetic models for charged transport

The transport equation. The initial value problem. The Boltzmann equation 
for diluted gases. Elementary properties of the solutions and rigorous 
validity. The H-theorem. Boundary conditions.   The Poisson equation. 
Collision operators. Existence results for initial-boundary value problems 
for Boltzmann-Poisson systems.

From kinetic to fluid dynamical models

Small mean free path, Hilbert and Chapmann expansions. Moment Methods.
Derivation of fluid level equations. 
Low field approximations: Drift-Diffusion models. 
High field approximations. Hydrodynamic models. 
The initial--boundary value problem. Steady state solutions. 
Regularity of solutions.

Prerequisite: Knowledge of some Real and Functional Analysis and basic PDE's
The following is a ``Suggested  Bibliography''

Cercignani C., 
``The Boltzmann Equation and its Applications''
Springer, New York,  1988.

Cercignani C., Illner, R. and Pulverenti, M.,  
``The Mathematical Theory of Diluted Gases''
Springer, New York,  1994. 

Ben Abdallah and Degond P.,  
On a hierarchy of macroscopic models for semiconductors
J. Math. Phys. {\bf 37} (7) (1996), 3306--3333.

Jerome, J.W., 
``Analysis of Charged Transport:
A Mathematical Study of Semiconductor Devices''
Springer, 1996. 

Markovich, P., Ringhofer, C.A., and Schmeiser, C.,  
``Semiconductor Equations''
Springer, Wien-New York, 1989.

Several recent papers on Boltzmann-Poisson systems in 
bounded domains. To be distributed in class.