Finite Domain Effects in Steady State Solutions of Poisson--Nernst--Planck Equations

DOI10.1137/18M1185946zbMath1434.35205arXiv1805.03332MaRDI QIDQ5231207

Doron Elad, Nir Gavish

Publication date: 26 August 2019

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03332

zbMATH Keywords

singular perturbationsPoisson-Nernst-Planckmatched asymptotic expansionfinite domain effectsrange-splitting

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Ill-posed problems for PDEs (35R25) Asymptotic expansions of solutions to PDEs (35C20) Boltzmann equations (35Q20) Electrochemistry (78A57)

Related Items (3)

The time decay rates of the classical solution to the Poisson-Nernst-Planck-Fourier equations in \(\mathbb{R}^3\) ⋮ Domain-size effects on boundary layers of a nonlocal sinh-Gordon equation ⋮ From stepwise integrations and low-rank updates to a pseudospectral solution operator matrix for the Helmholtz operator \(\frac{d}{dx} a(x) \frac{d}{dx} + c(x)\)

Cites Work

• Unnamed Item
• Boundary layer solutions of charge conserving Poisson-Boltzmann equations: one-dimensional case
• New Poisson–Boltzmann type equations: one-dimensional solutions
• A Poisson–Nernst–Planck Model for Biological Ion Channels—An Asymptotic Analysis in a Three-Dimensional Narrow Funnel
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
• On the structure of generalized Poisson–Boltzmann equations
• The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle
• Current-Voltage Relations for Electrochemical Thin Films
• Two- and three-dimensional Poisson--Nernst--Planck simulations of current flow through gramicidin A

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