The asymptotic behavior and the quasineutral limit for the bipolar Euler-Poisson system with boundary effects and a vacuum

Abstract

In this paper, a one-dimensional bipolar Euler-Poisson system (a hydrodynamic model) from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy’s law time asymptotically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L ^∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the corresponding one-dimensional compressible Euler equations with damping exponentially fast as t → +∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.

Keywords

Bipolar hydrodynamic model / Asymptotic behavior / Quasineutral limit / Entropy / Energy estimate

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