Poisson-Nernst-Planck equations with steric effects -- non-convexity and multiple stationary solutions

DOI10.1016/J.PHYSD.2017.12.008zbMath1381.35187arXiv1703.07164OpenAlexW2607342267MaRDI QIDQ1699518

Nir Gavish

Publication date: 23 February 2018

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.07164

zbMATH Keywords

multiple solutionsion channelsPNP-Cahn-Hilliard equationsPoisson-Nernst-Planck equations with steric effectssteric effects

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

A positive and energy stable numerical scheme for the Poisson-Nernst-Planck-Cahn-Hilliard equations with steric interactions ⋮ Poisson-Nernst-Planck equations with high-order steric effects ⋮ Large deviations and gradient flows for the Brownian one-dimensional hard-rod system ⋮ Positivity preserving finite difference methods for Poisson-Nernst-Planck equations with steric interactions: application to slit-shaped nanopore conductance ⋮ Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations ⋮ Thin layer analysis of a non-local model for the double layer structure ⋮ Global existence of solutions for the Poisson-Nernst-Planck system with steric effects

Uses Software

• ode45
• pde2path

Cites Work

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• Multiple solutions of steady-state Poisson–Nernst–Planck equations with steric effects
• On the structure of generalized Poisson–Boltzmann equations
• Spatially Localized Self-Assembly Driven by Electrically Charged Phase Separation
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Justification of the Ginzburg–Landau approximation for an instability as it appears for Marangoni convection
• Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges
• New instabilities in two-dimensional rotating convection and magnetoconvection

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