本项目旨在研究二维定常可压亚音速—音速Euler-Poisson流的适定性，包括不含松弛效应的Euler-Poisson管道流和含有松弛效应的半导体Euler-Poisson流。在数学上，解决这些问题需要求解拟线性椭圆型耦合方程组或拟线性椭圆—双曲耦合方程组的定解问题，控制方程所具有的非局部和非线性的耦合关系等性质给这些问题的数学研究带来了困难，研究这类数学问题的理论和工具还不够完善，我们将针对具体的问题，提出符合物理背景的定解问题和解的定义，研究和探索解的存在性、唯一性以及正则性等的性质。

The project deals with two-dimensional subsonic-Soinc Euler-Poisson flows, including Euler-Poisson flows without relaxation effects in nozzels and Euler-Poisson flows with relaxation effects for semiconductors. From the view of mathematics, solving these problems is equal to solving the definite solutions problems of coupled quasilinear elliptic partial differential systems or coupled quasilinear elliptic-hyperbolic partial differential systems of mixed type, and the nonlocal and nonlinear way the governing equations coupled and other properties bring difficulties to mathematical research. The theory and tools for studying such mathematical problems are not complete. Our target is to establish reasonable definite problem and the definition of solution which satisfy physical interpretations for each specific problem, and to investigate and explore the existence, uniqueness, regularity and other properties of the solutions.