Existence and asymptotics of solutions of the Debye-Nernst-Planck system   in R^2
  In this paper we investigate a system describing electrically charged particles in the whole space R^2. Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions. 
A. Herczak and M. Olech