粘性量子流体动力学模型定态解的渐进极限

Asymptotic Limits of Steady-state Viscous Quantum Hydrodynamic Model

研究了在一维空间的半导体量子流体动力学模型，其定态问题可化为四阶方程或二阶方程来解决解的存在性及渐进极限。利用椭圆型方程的估计，得到定态问题的解的范数估计，从而可进行了粘性消失的极限和Dispersion极限。

In this paper,the steady-state quantum hydrodynamic model for semiconductors was analyzed on the one dimensional space.The steady-state system was transformed into a fourth-order problem or a second-order system to solve the existence and get the asymptotic limits. Applying the estimates of the elliptic equation,some norm estimates can be obtained.Thus,viscosity vanishing limit and dispersion limit can be carried out.