Non-localness of excess potentials and boundary value problems of Poisson-Nernst-Planck systems for ionic flow: a case study

DOI10.1007/s10884-017-9578-2zbMath1407.34071OpenAlexW2582702309MaRDI QIDQ1663182

Weishi Liu, Li-Li Sun

Publication date: 21 August 2018

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-017-9578-2

zbMATH Keywords

boundary value problemsionic flowsnonlocal excess potentialsPoisson-Nernst-Planck (PNP) type systems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60) Motion of charged particles (78A35)

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Cites Work

• Unnamed Item
• A mathematical model for the hard sphere repulsion in ionic solutions
• Poisson-Nernst-Planck systems for narrow tubular-like membrane channels
• Asymptotic expansions and numerical simulations of I-V relations via a steady state Poisson-Nernst-Planck system
• Theory of functional differential equations. 2nd ed
• Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
• Introduction to functional differential equations
• Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis
• Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics
• A complete analysis of a classical Poisson-Nernst-Planck model for ionic flow
• One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species
• Poisson--Nernst--Planck Systems for Ion Flow with a Local Hard-Sphere Potential for Ion Size Effects
• Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
• A Poisson–Nernst–Planck Model for Biological Ion Channels—An Asymptotic Analysis in a Three-Dimensional Narrow Funnel
• Continuum electrostatics for ionic solutions with non-uniform ionic sizes
• Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
• Ion Flow through Narrow Membrane Channels: Part I
• Ion Flow through Narrow Membrane Channels: Part II
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Mathematical Study
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
• Kinetic Theory of Granular Gases
• Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
• Current-Voltage Relations for Electrochemical Thin Films
• Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges
• Reversal permanent charge and reversal potential: case studies via classical Poisson–Nernst–Planck models
• Two- and three-dimensional Poisson--Nernst--Planck simulations of current flow through gramicidin A

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