A singularly perturbed nonlinear Poisson-Boltzmann equation: uniform and super-asymptotic expansions

DOI10.1002/mma.3593zbMath1336.35038OpenAlexW1522646962MaRDI QIDQ2793954

Victor A. Kovtunenko, Klemens Fellner

Publication date: 17 March 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3593

zbMATH Keywords

porous medianonlinear Poisson equationBoltzmann statisticselectro-chemistryphotovoltaicsteady-state Poisson-Nernst-Planck systemsuper-asymptotics

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Electrochemistry (78A57) PDEs in connection with statistical mechanics (35Q82)

Related Items (6)

Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems ⋮ Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium ⋮ On generalized Poisson-Nernst-Planck equations with inhomogeneous boundary conditions: a-priori estimates and stability ⋮ Entropy method for generalized Poisson-Nernst-Planck equations ⋮ Perturbation solutions for the nonlinear Poisson-Boltzmann equation with a high-order-accuracy Debye-Hückel approximation ⋮ A discontinuous Poisson–Boltzmann equation with interfacial jump: homogenisation and residual error estimate

Cites Work

• Unnamed Item
• Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients
• A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain
• Non-homogeneous media and vibration theory
• Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries
• From shape variation to topological changes in constrained minimization: a velocity method-based concept
• Depth Averaged Analytic Solution for a Laminar Flow Fuel Cell with Electric Double Layer Effects
• Semilinear elliptic Neumann problems with rapid growth in the nonlinearity
• Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
• A DRIFT–DIFFUSION–REACTION MODEL FOR EXCITONIC PHOTOVOLTAIC BILAYERS: ASYMPTOTIC ANALYSIS AND A 2D HDG FINITE ELEMENT SCHEME
• Asymptotic analysis of the Poisson–Boltzmann equation describing electrokinetics in porous media
• High Precision Identification of an Object: Optimality-Conditions-Based Concept of Imaging
• Asymptotic treatment of perforated domains without homogenization

This page was built for publication: A singularly perturbed nonlinear Poisson-Boltzmann equation: uniform and super-asymptotic expansions