摘要
In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar QHD models tends to the equilibrium state at an exponential decay rate for the multi-dimensional cases. The arguments is based on a series of a priori estimates.
In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar QHD models tends to the equilibrium state at an exponential decay rate for the multi-dimensional cases. The arguments is based on a series of a priori estimates.
