Asymptotic behavior and classical limit of the solutions to quantum hydro dynamic model for semiconductors

摘要

The main purpose of this short paper is to show the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one-dimensional quantum hydrodynamic model of semiconductors. We also study a singular limit from this model to the classical hydrodynamic model. This limit is called a classical limit. In this paper, we briefly discuss the results in our paper [14].