Quasi-Neutral Limit Of One-Dimensional Bipolar Steady State HD Model

In semiconductor physics,the classical HD model is used to describe the transport of charged particle flow in semiconductor devices.From a mathematical point of view,it is coupled by the damped Euler equation system and the Poisson equation satisfied by the electric potential.The purpose of this paper is to extend Peng[19]research results on quasi-neutral limit problem of one-dimensional isentropic unipolar steady-state HD model to bipolar case.So we consider the quasi-neutral limit problem of the isentropic bipolar steady-state HD model and obtain the following main results.First,based on the idea of asymptotic expansion,we first expand the irrotational flow of the above problem in the form of Debye length lambda in the interior and near the boundary of a given region.Then,using the standard matching technique,the equations satisfying the internal function and the boundary layer function are derived.Secondly,For one-dimensional case,we have successfully established the existence and uniqueness of zero-order boundary layer function with exponential decay property and zero-order error function by applying the central manifold theorem and the famous Schauder fixed point theorem in dynamic system theory,respectively.On this basis,it is proved by detailed calculus that when lambda? 0 the subsonic non-swirling flow converges strongly to the zero-order approximate solution in the sense of L? module and the corresponding error estimates are given.