Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma

Masahiro  Suzuki

doi:10.3934/krm.2016008

Article Contents

2016, Volume 9, Issue 3: 587-603. Doi: 10.3934/krm.2016008

This issue Previous Article A kinetic reaction model: Decay to equilibrium and macroscopic limit Next Article Entropy production for ellipsoidal BGK model of the Boltzmann equation

Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma

Masahiro Suzuki^1,

1.
Department of Computer Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555

Received: March 31, 2015

Revised: January 31, 2016

Published: August 2016

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Abstract

The main concern of this paper is to analyze a boundary layer called a sheath that occurs on the surface of materials when in contact with a multicomponent plasma. For the formation of a sheath, the generalized Bohm criterion demands that ions enter the sheath region with a high velocity. The motion of a multicomponent plasma is governed by the Euler--Poisson equations, and a sheath is understood as a monotone stationary solution to those equations. In this paper, we prove the unique existence of the monotone stationary solution by assuming the generalized Bohm criterion. Moreover, it is shown that the stationary solution is time asymptotically stable provided that an initial perturbation is sufficiently small in weighted Sobolev space. We also obtain the convergence rate, which is subject to the decay rate of the initial perturbation, of the time global solution toward the stationary solution.

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Mathematics Subject Classification: Primary: 35L04, 35J65, 35B40, 82D10.

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References

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