On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method

Abstract

We consider a one-dimensional, monocharged plasma as described by the Vlasov--Poisson system and investigate the behaviour of the solutions for large times. Using a rescaling method we are able to determine an explicit solution of the system which corresponds to a globally attractive steady state for the rescaled system. We investigate in which sense and at which rate the solutions of the rescaled system converge to this global attractor and interpret the results for the original system.