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| The Asymptotic Behavior and the Quasineutral Limit forthe Bipolar Euler-Poisson System withBoundary Effects and a Vacuum |
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Citation： |
Yeping LI.The Asymptotic Behavior and the Quasineutral Limit forthe Bipolar Euler-Poisson System withBoundary Effects and a Vacuum[J].Chinese Annals of Mathematics B,2013,34(4):529~540 |
| Page view： 1666
Net amount： 1573 |
Authors： |
Yeping LI; |
Foundation： |
National Natural Science Foundation of China (No. 11171223) and the InnovationProgram of Shanghai Municipal Education Commission (No. 13ZZ109). |
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| 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 |
Classification： |
35M20, 35Q35, 76W05 |
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