The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors

In this paper, we are concerned with the large-time behavior of the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers (electrons or holes) in semiconductor device. For the Cauchy problem in R-3, the global existence and uniqueness of smooth solutions, when the initial data are small perturbations of an equilibrium state, are obtained. Also, the solutions tend to the corresponding equilibrium state exponentially fast as the time tends to infinity. The analysis is based on the elementary L-2-energy method, but various techniques are introduced to establish a priori estimates.