Asymptotic Behavior Of Smooth Solutions To Bipolar Hydrodynamic Model

In this paper,we mainly study the asymptotic behavior of the solutions to the bipolar hydrodynamic for semiconductor:where x ? Rd(d ? 1)is the space variable,t ? R+[0,?)is the time variable.This paper is divided into four chapters.In the first chapter,we firstly intro-duced the physical background and significance of studying bipolar semiconductor hydrodynamic model.Then,the research status of bipolar semiconductor hydrody-namic model is reviewed.In the second chapter,we introduced some preparatory knowledge.Firstly,the existence of steady-state solutions and the relevant con-clusions are quoted.Secondly,some symbols and basic Lemmas are expounded.In the third chapter,we proved that the smooth solution to the initial boundary value problem of the one-dimensional bipolar hydrodynamic model converges to the steady-state solutions with exponential rate.In the fourth chapter,we con-sidered that the smooth solution of the high dimensional bipolar hydrodynamic model convergence to constant equilibrium state with exponential rate.Unlike the one-dimensional case,in the estimation of higher order derivatives,we used the Lagrange multipliers to symmetric the original equation.