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Abstract： We study the onedimensional quantum hydrodynamic system for semiconductors.It takes the isentropic EulerPoisson equations with the quantum potential and momentum relaxation term in the momentum equations.We show the asymptotic behavior of the solutions for the initial value problem to onedimensional quantum EulerPoisson equations，when the far field states of the current density are inconsistent and the far field of the electric field is not zero.Choosing proper corrections and using the energy methods，we prove that the solutions of onedimensional isentropic quantum EulerPoisson equations decay exponentially fast to the stationary solutions.This result improves previous results in which the current density′s far fields are equal and the far field of the electric field is zero.
Key words： asymptotic behavior； quantum EulerPoisson equation； energy estimate； stationary solutions
CLC number： O 175.2Document code： AArticle ID： 10005137（2013）06055114
Received date： 20130926
Foundation item： Supported by the National Science Foundation of China （11171223） and the Innovation Program of Shanghai Municipal Education Commission （13ZZ109）.
Biography： Li Yeping（1972-），male，professor，College of Mathematics and Sciences，Shanghai Normal University；Pu Fenfang（1987-），female，graduate student，College of Mathematics and Sciences，Shanghai Normal University.
*Corresponding author1Introduction
We study the following isentropic quantum EulerPoisson equations in spatial one
and t>0.Here n，j， and E represent the density，the momentum and the electric field，respectively.The function b（x） stands for the density of fixed，positively charged background ions，the socalled doping profile.The positive constant ε is called the scaled Planck constant.The coefficient τ denotes the relaxation time.The function p（n） is the pressure.For more details of model，refer to[1-4].
Due to their physical importance，mathematical complexity and wide range of applications，there are many studies on the wellposedness and largetime behavior of the solutions of the quantum EulerPoisson equations，such as[5-14]and the references therein.In this paper，we will study the largetime behavior of the solutions for the initial value problem to onedimensional quantum EulerPoisson equations when the far field states of the current density are inconsistent and the far field of the electric field is not zero.Since our interest here is the long behavior of the solutions，without loss of generality，we assume that
Key words： asymptotic behavior； quantum EulerPoisson equation； energy estimate； stationary solutions
CLC number： O 175.2Document code： AArticle ID： 10005137（2013）06055114
Received date： 20130926
Foundation item： Supported by the National Science Foundation of China （11171223） and the Innovation Program of Shanghai Municipal Education Commission （13ZZ109）.
Biography： Li Yeping（1972-），male，professor，College of Mathematics and Sciences，Shanghai Normal University；Pu Fenfang（1987-），female，graduate student，College of Mathematics and Sciences，Shanghai Normal University.
*Corresponding author1Introduction
We study the following isentropic quantum EulerPoisson equations in spatial one
and t>0.Here n，j， and E represent the density，the momentum and the electric field，respectively.The function b（x） stands for the density of fixed，positively charged background ions，the socalled doping profile.The positive constant ε is called the scaled Planck constant.The coefficient τ denotes the relaxation time.The function p（n） is the pressure.For more details of model，refer to[1-4].
Due to their physical importance，mathematical complexity and wide range of applications，there are many studies on the wellposedness and largetime behavior of the solutions of the quantum EulerPoisson equations，such as[5-14]and the references therein.In this paper，we will study the largetime behavior of the solutions for the initial value problem to onedimensional quantum EulerPoisson equations when the far field states of the current density are inconsistent and the far field of the electric field is not zero.Since our interest here is the long behavior of the solutions，without loss of generality，we assume that