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Prof. Li Chen  ( Tsinghua University, China )

2008 - 07 - 08 (Tue.)
11:00 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk I will first give a brief introduction on the mathematical models in semiconductor simulation including classical and quantum models, microscopic and macroscopic models. Then I will switch to one of the macroscopic quantum models, the so called QDD model. We will show a series of results obtained recently, including the existence, semi-classical limit and long-time behavior of weak solutions to this kind of models. Our methods are based on semi-discretization in time for the approximation scheme and entropy estimates for compactness argument. The results on QDD model are joint works with X.Chen and Q.Ju.