# American Institute of Mathematical Sciences

September  2012, 17(6): 1939-1967. doi: 10.3934/dcdsb.2012.17.1939

## On the structure of double layers in Poisson-Boltzmann equation

 1 ICMAT (CSIC-UAM-UC3M-UCM), C/Nicolás Cabrera 15, Madrid, 28049 2 Instituto de Ciencias Matemáticas (CSIC - UAM - UC3M - UCM), C/Nicolás Cabrera, 13-15, Campus de Cantoblanco, 28049 Madrid, Spain

Received  May 2011 Revised  September 2011 Published  May 2012

We study the solutions to Poisson-Boltzmann equation for electrolytic solutions in a domain $\Omega$, surrounded by an uncharged dielectric medium. We establish existence, uniqueness and regularity of solutions and study in detail their asymptotic behaviour close to $\partial\Omega$ when a characteristic length, called the Debye length, is sufficiently small. This is a double layer with a thickness that changes from point to point along $\partial\Omega$ depending on the normal derivative of a harmonic function outside $\Omega$ and the mean curvature of $\partial\Omega$. We also provide numerical evidence of our results based on a finite elements approximation of the problem.
Citation: Marco A. Fontelos, Lucía B. Gamboa. On the structure of double layers in Poisson-Boltzmann equation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1939-1967. doi: 10.3934/dcdsb.2012.17.1939
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