The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

DOI10.1063/1.4878492zbMath1294.35053OpenAlexW2306285730MaRDI QIDQ5171350

Chiun-Chang Lee

Publication date: 26 July 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4878492

zbMATH Keywords

maximum principleregularityweak solutionsRobin boundary conditionPoisson-Boltzmann equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Variational methods applied to PDEs (35A15) Maximum principles in context of PDEs (35B50) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Related Items (11)

Boundary asymptotics for a non-neutral electrochemistry model with small Debye length ⋮ Global regularity for Nernst–Planck–Navier–Stokes systems with mixed boundary conditions ⋮ A Maxwell–Ampère Nernst–Planck Framework for Modeling Charge Dynamics ⋮ Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model ⋮ Domain-size effects on boundary layers of a nonlocal sinh-Gordon equation ⋮ Thin layer analysis of a non-local model for the double layer structure ⋮ Very weak solutions for Poisson-Nernst-Planck system ⋮ Global existence of solutions for the Poisson-Nernst-Planck system with steric effects ⋮ Debye layer in Poisson-Boltzmann model with isolated singularities ⋮ Finite Domain Effects in Steady State Solutions of Poisson--Nernst--Planck Equations ⋮ Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

Cites Work

• Boundary asymptotics for solutions of the Poisson-Boltzmann equation
• Mathematical models for the deformation of electrolyte droplets
• On electro-kinetic fluids: one-dimensional configurations
• New Poisson–Boltzmann type equations: one-dimensional solutions
• On the Robin Boundary Condition for Laplace's Equation in Lipschitz Domains
• Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
• Counterion Condensation as an Exact Limiting Property of Solutions of the Poisson–Boltzmann Equation
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
• Current-Voltage Relations for Electrochemical Thin Films

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