THE INFLUENCE OF SMALL PERMANENT CHARGES AND PARTIAL BOUNDARY CONDITIONS ON INDIVIDUAL FLUXES VIA POISSON-NERNST-PLANCK SYSTEMS

Yiwei Wang; Lijun Zhang

doi:10.11948/20250367

2026 Volume 16 Issue 4

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Yiwei Wang, Lijun Zhang. THE INFLUENCE OF SMALL PERMANENT CHARGES AND PARTIAL BOUNDARY CONDITIONS ON INDIVIDUAL FLUXES VIA POISSON-NERNST-PLANCK SYSTEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2218-2237. doi: 10.11948/20250367

Citation:

Yiwei Wang, Lijun Zhang. THE INFLUENCE OF SMALL PERMANENT CHARGES AND PARTIAL BOUNDARY CONDITIONS ON INDIVIDUAL FLUXES VIA POISSON-NERNST-PLANCK SYSTEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2218-2237. doi: 10.11948/20250367

THE INFLUENCE OF SMALL PERMANENT CHARGES AND PARTIAL BOUNDARY CONDITIONS ON INDIVIDUAL FLUXES VIA POISSON-NERNST-PLANCK SYSTEMS

Yiwei Wang^1,2,,
Lijun Zhang^2,3, ,

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266510, China
2.
School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China
3.
Material Science, Innovation and Modelling Research Focus Area, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Author Bio: Email: yiwei_1223@163.com(Y. Wang)
Corresponding author: Email: li-jun0608@163.com(L. Zhang)

Abstract

Abstract

We investigate ionic flow through membrane channels within a one-dimensional Poisson-Nernst-Planck framework, considering two oppositely charged ion species and incorporating a small but non-zero permanent charge. Building upon prior analysis in [50], which was confined to cases with higher left-side concentrations, we relax this constraint to examine a broader and more physiologically relevant range of boundary conditions. Crucially, instead of considering the product of zeroth- and first-order terms in the flux expansion, we focus on the first-order term itself, which directly captures the leading effects of channel geometry and permanent charge. Under partial electroneutral boundary conditions, our analysis results demonstrate that the permanent charge plays a regulatory role: It can either enhance or suppress both ion fluxes simultaneously, or exert opposing effects by increasing anion flux while decreasing cation flux - an outcome that depends on the electric potential applied at the boundary. We further identify and compare several critical electric potentials, providing new insights into the transport mechanisms operative across different potential intervals. Numerical simulations on selected cases yield results in excellent agreement with the theory, confirming and supporting our analytical conclusions.
- PNP systems /
- permanent charges /
- individual fluxes /
- partial boundary conditions
MSC: 34A26, 34B16, 34D15, 37D10, 92C35

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References

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