Non-localness of excess potentials and boundary value problems of Poisson-Nernst-Planck systems for ionic flow: a case study
type: Item
instance of: scholarly article
title: Non-localness of excess potentials and boundary value problems of Poisson-Nernst-Planck systems for ionic flow: a case study
zbMATH Open document ID: 1407.34071
author: Weishi Liu
author: Li-Li Sun
published in: Journal of Dynamics and Differential Equations
publication date: 2018-08-21T00:00:00Z
review text: In this paper, a form of natural boundary conditions is presented, so that the corresponding boundary value problems (BVP) of Poisson-Nernst-Planck (PNP) type systems with nonlocal excess potentials are generally well-posed. PNP type systems are basic primitive models for ionic flow through ion channels. Important properties of ion channels, such as current-voltage relations, permeation and selectivity, can be extracted from solutions of BVP of PNP type models. Many issues of BVP of PNP type systems with local excess potentials (including particularly classical PNP systems that treat ions as point-charges) are extensively examined analytically and numerically. On the other hand, for PNP type systems with nonlocal excess potentials, even the issue of well-posedness of BVP is poorly understood. In fact, the formulation of correct boundary conditions seems to be overlooked, even though complications of ionic behavior near the boundaries (locations of applied electrodes) have been long experienced in experiments and simulations. PNP type systems with nonlocal excess potentials can be viewed as functional differential systems and, for many approximation models of nonlocal excess potentials, as differential equations with both delays and advances. Thus, PNP type systems with nonlocal excess potentials have infinite degree of freedoms and BVP with the traditional two-point-boundary-conditions would be severely under determined. The mathematical theory for PNP with nonlocal excess potential would be significantly different from that for PNP with local excess potentials. This work, at an early stage toward a better understanding of related issues, provides some insights on interpretations of experimental designs of imposing boundary conditions and for correct formulations of numerical simulations.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 78A35
zbMATH DE Number: 6921348
zbMATH Keywords: ionic flows
zbMATH Keywords: nonlocal excess potentials
zbMATH Keywords: boundary value problems
zbMATH Keywords: Poisson-Nernst-Planck (PNP) type systems
MaRDI profile type: Publication
full work available at URL: s10884-017-9578-2
OpenAlex ID: W2582702309
cites work: Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
cites work: Current-Voltage Relations for Electrochemical Thin Films
cites work: Ion Flow through Narrow Membrane Channels: Part I
cites work: Ion Flow through Narrow Membrane Channels: Part II
cites work: Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
cites work: Q5783108
cites work: Kinetic Theory of Granular Gases
cites work: Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges
cites work: Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models
cites work: Theory of functional differential equations. 2nd ed
cites work: Introduction to functional differential equations
cites work: Two- and three-dimensional Poisson--Nernst--Planck simulations of current flow through gramicidin A
cites work: A mathematical model for the hard sphere repulsion in ionic solutions
cites work: Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
cites work: Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis
cites work: Continuum electrostatics for ionic solutions with non-uniform ionic sizes
cites work: Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
cites work: One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species
cites work: Poisson-Nernst-Planck systems for narrow tubular-like membrane channels
cites work: Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics
cites work: Poisson-Nernst-Planck systems for ion flow with a local hard-sphere potential for ion size effects
cites work: A complete analysis of a classical Poisson-Nernst-Planck model for ionic flow
cites work: Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Mathematical Study
cites work: A Poisson–Nernst–Planck Model for Biological Ion Channels—An Asymptotic Analysis in a Three-Dimensional Narrow Funnel
cites work: Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
cites work: Asymptotic expansions and numerical simulations of I-V relations via a steady state Poisson-Nernst-Planck system
DOI: 10.1007/S10884-017-9578-2
description: scientific article; zbMATH DE number 6921348