Self-similar solutions for the two-dimensional Nernst–Planck–Debye system

Volume 39 / 2012

Łukasz Paszkowski Applicationes Mathematicae 39 (2012), 329-338 MSC: 35B40, 35K40, 35J60. DOI: 10.4064/am39-3-7


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.


  • Łukasz PaszkowskiInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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