SINGULARITIES OF STATIONARY SOLUTIONS TO THE VLASOV–POISSON SYSTEM IN A POLYGON

Abstract

We present an existence result for the stationary Vlasov–Poisson system in a bounded domain of ℝN, with more general hypotheses than considered so far in the literature. In particular, we prove the equivalence of the kinetic approach (which consists in looking for the equilibrium distribution function) and the potential approach (where the unknown is the electrostatic potential at equilibrium). We study the dependence of the solution on parameters such as the total mass of the distribution, or those entering in the boundary conditions of the potential. Focusing on the case of a plane polygon, we study the singular behavior of the solution near the re-entrant corners, and examine the dependence of the singularity coefficients on the parameters of the problem. Numerical experiments illustrate and confirm the analysis.