Existence and asymptotics of solutions of the Debye-Nernst-Planck system in R^2

TL;DR

This paper studies the long-term behavior of solutions to the Debye-Nernst-Planck system in two-dimensional space, focusing on small initial data and using radially symmetric self-similar solutions to analyze asymptotics.

Contribution

It establishes the existence and asymptotic properties of solutions for the Debye-Nernst-Planck system in R^2, emphasizing the role of self-similar solutions for small initial data.

Findings

Existence of solutions for small initial data

Characterization of large-time asymptotics using self-similar solutions

Radial symmetry plays a key role in analysis

Abstract

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.