Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 510-522.

• Articles • Previous Articles     Next Articles

Global Existence and Asymptotic Behavior of Smooth Solutions to the IBVP for the 3D Bipolar Euler-Poisson System

 MAO Jian-Feng1, LI Ye-Ping2*   

  1. 1.School of Mathematics and Statistics, Hubei University of Science and Technology, Hubei Xianning 437100;
    2.Department of Mathematics, Shanghai Normal University, Shanghai 200234
  • Received:2011-10-13 Revised:2012-12-05 Online:2013-06-25 Published:2013-06-25
  • Contact: LI Ye-Ping,ypleemei@yahoo.com.cn E-mail:ypleemei@yahoo.com.cn
  • Supported by:

    国家自然科学基金(11171223)和上海市教委创新重点项目(13ZZ109)资助

Abstract:

In this paper, we study a three-dimensional (3D) bipolar Euler-Poisson system (hydrodynamic model) from semiconductors and plasmas. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. We first proved global existence and uniqueness of classical solutions to the initial boundary value problem (IBVP) with slip boundary condition and Nemann boundary condition when the initial data is near its equilibrium. As the by-product, we also show asymptotic behavior of IBVP for the three-dimensional bipolar Euler-Poisson system. That is, the density of two particles (electron and hole or positive and negative ion) is verified to satisfy the porous medium equation and the current momentums obey to the classical Darcy's law.

Key words: Global existence, Bipolar, Euler-Poisson system, Energy estimates, Asymptotic behavior

CLC Number: 

  • 35M20
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