Analysis Of Subsonic Steady-state Solutions For Semiconductor HD Models

In this paper,we study the well-posedness of the subsonic steady-state solu-tion of one-dimensional hydrodynamics model of semiconductor with sonic bound-ary.It includes the existence,uniqueness and optimal regularization analysis of subsonic solutions.In the conventional Euler-Poisson equation,the momentum relaxation time ? is a constant.In this paper,we assume that ?=?(n),the momentum relaxation time,is a function of electron density and satisfies certain conditions.The subsonic solution of one-dimensional semiconductor hydrodynam-ics model is studied under this condition.We can solve this problem by using the non-degenerate equation of the original equation.Then,the existence and uniqueness of subsonic solution of approximate equation is obtained by using Schauder fixed point theorem and elliptic L2 theo-ry.Finally,the unique subsonic solution of the original equation is obtained by compactness analysis.And we further prove that it have good regularity.