1. A singularly perturbed nonlinear Poisson-Boltzmann equation: uniform and super-asymptotic expansions.
- Author
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Fellner, Klemens and Kovtunenko, Victor A.
- Subjects
- *
POISSON algebras , *BOLTZMANN'S equation , *POROUS materials , *SINGULAR perturbations , *PHOTOVOLTAIC power generation - Abstract
A steady-state Poisson-Nernst-Planck system is investigated, which is conformed into a nonlinear Poisson equation by means of the Boltzmann statistics. It describes the electrostatic potential generated by multiple concentrations of ions in a heterogeneous (porous) medium with diluted (solid) particles. The nonlinear elliptic problem is singularly perturbed with the Debye length as a small parameter related to the electric double layer near the solid particle boundary. For star-shaped solid particles, we prove rigorously that the solution of the problem in spatial dimensions 1d, 2d and 3d is uniformly and super-asymptotically approximated by a constant reference state. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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