【摘要】 研究了一类一维稳态双极半导体方程的粘滞量子流体力学模型.该模型包含关于粒子浓度和电流密度的连续方程以及电势Poisson方程的耦合方程组,其中含有三阶量子修正项和二阶粘滞项.该问题在有界区间(0,1)中讨论,并通过边界条件的假设将原方程组变形为常见的形式,得到原问题的等价问题.用截断方法将等价问题正则化,并得到正则化问题解的先验估计.利用Leray-Schauder不动点定理证明正则化问题解的存在性,最后通过L∞估计证明正则化问题的解即为原问题的解,从而证明了原双极粘滞量子流体力学模型存在稳态解.更多还原

【Abstract】 The steady-state bipolar viscous quantum hydrodynamic model in one space dimension was studied.The model consists of the continuity equations for the particles and current densities,coupled with the Poisson equation for the electrostatic potential.The problem is considered within a bounded interval(0,1) and simplified to a common one under the assumption of the boundary conditions.With the truncation method the tantamount problem is regularized and the prior estimate of its solutions is obtained.Then the existence of the solutions to the regular problem is proved by the Leray-Schauder fixed-point theorem.In the end,the solutions are proved just to be the solutions of the original problem by the L∞ estimate.Then the existence of solutions to the bipolar viscous quantum hydrodynamic model is acquired.更多还原