NONLINEAR STABILITY OF BOUNDARY LAYER SOLUTIONS TO THE EULER-POISSON EQUATIONS IN PLASMA PHYSICS

摘要

The main concern of the present paper is to study a boundary layer, called sheath, which appears over a material in contact with plasma. The Bohm criterion in plasma physics claims the velocity of positive ions should be faster than a certain value for the formation of a sheath. The behavior of the plasma is governed by the Euler-Poisson equations. Mathematically, we define the sheath by a monotone stationary solution to the system over a half space. We first derive conditions for the existence of the stationary solution and observe that the Bohm criterion with certain physically reasonable conditions are sufficient for the existence of the stationary solution. Then we discuss its asymptotic stability under the Bohm criterion by using the weighted energy method. We also obtain convergence rates subject to the spatial decay rates of the initial perturbation.