We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-7,
author = {\L ukasz Paszkowski},
title = {Self-similar solutions for the two-dimensional Nernst-Planck-Debye system},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {329-338},
zbl = {1252.35105},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-7}
}
Łukasz Paszkowski. Self-similar solutions for the two-dimensional Nernst-Planck-Debye system. Applicationes Mathematicae, Tome 39 (2012) pp. 329-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-7/