Abstract of the Talk
In this talk, we present our new results on stability and semi-classical limit for a semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping profile. The FQHD model can be used to analyze the influence of both thermal effect and quantum effect on the motion of electrons in semiconductor device. We consider the initial-boundary value problem of this model in a one-dimensional bounded domain and adopt the quantum vanishing Ohm contact boundary condition. Firstly, the existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and Schauder fixed-point theorem. The most difficult point is to obtain the bounded estimate. Secondly, we show the asymptotic stability of the stationary solution by using an elementary energy method but with some new developments. Finally, the semi-classical limit is considered for both stationary solution and global solution by using the energy method again. This is a joint work with Prof. Kaijun Zhang.
Biography of the Speaker
Haifeng Hu obtained his Ph.D. from Northeast Normal University in 2015. Now he is Research Associate of Center for Partial Differential Equations at East China Normal University. His research interests are partial differential equations and their applications, especially hydrodynamic model for semiconductors.