一类单极等熵流体动力学半导体模型的松弛极限

Relaxation Limit of a Unipolar Isentropic Hydrodynamic Model for Semiconductors

对一类有短的动量松弛时间的多维等熵流体动力学半导体模型的极限问题进行了讨论．首先构造非线性问题的有初始层的近似解,进而,在归结问题的解存在且有合适的正则性的假设下,证明了原非线性问题的局部古典解的存在性,并且证明了这个解在归结问题解的存在时间区间内收敛到形式近似解．

This note is concerned with the unipolar isentropic hydrodynamical models for semiconductors with short momentum relaxation time in serval space variables. The author first constructs formal approximations of the initial layer solution to the nonlinear problem. Furthermore, assuming some regularity of the solution to the reduced problem, and proves the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval.