The Uniqueness Of Supersonic Solution Of Hydrodynamic Model For Semiconductors

In this paper,we try to prove the uniqueness of supersonic steady solution of hydro-dynamic model for semiconductors with sonic boundary conditions.This question is not clear and very difficulty relative to the uniqueness of subsonic solution,we analyze this question by the phase plane and some transformation of integration to calculate the length of the electron move in the supersonic,then we can get the conclusion.For the case that without the effect of the electron,that is,the Euler-Poisson equa-tion(relaxation time ?= ?),we obtained the uniqueness of the solution;but when with the effect of electron,we can only prove for the situation when ? large or doping profile b large that the conclusion is still right.