Very weak solutions for Poisson-Nernst-Planck system

被引：4

作者：

Hineman, Jay L. ^{[1
]}

Ryham, Rolf J. ^{[1
]}

机构：

[1] Fordham Univ, Dept Math, Bronx, NY 10458 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 115卷

关键词：

Poisson-Nernst-Planck; Drift-diffusion-Poisson; Stationary diffuse charge; ELLIPTIC-EQUATIONS; TIME BEHAVIOR; EXISTENCE; DISTANCE; RESPECT; FLUIDS;

D O I：

10.1016/j.na.2014.11.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We formulate a notion of very weak solution for the Poisson-Nernst-Planck system. The stationary system possesses a local monotonicity formula. Iterative application of the formula reveals improvement in estimates for ion density and potential, and leads to a local boundedness result. Local boundedness extends to steady-state systems for multiple ions and variable coefficients. The formulation applies to the related Keller-Segel system where stationary very weak solutions in two dimensions are regular. Examples illustrate how structure influences this regularity in higher dimensions. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：12 / 24

页数：13

共 50 条

[21] Test of Poisson-Nernst-Planck theory in ion channels
Corry, B
Kuyucak, S
Chung, SH
JOURNAL OF GENERAL PHYSIOLOGY, 1999, 114 (04): : 597 - 599
[22] Error Analysis of Mixed Finite Element Method for Poisson-Nernst-Planck System
He, Mingyan
Sun, Pengtao
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2017, 33 (06) : 1924 - 1948
[23] A weak Galerkin finite element method for time-dependent Poisson-Nernst-Planck equations
Ji, Guanghua
Zhu, Wanwan
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 416
[24] Multiple solutions of steady-state Poisson-Nernst-Planck equations with steric effects
Lin, Tai-Chia
Eisenberg, Bob
NONLINEARITY, 2015, 28 (07) : 2053 - 2080
[25] Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality
Pabst, M.
JOURNAL OF CHEMICAL PHYSICS, 2014, 140 (22):
[26] Introduction of effective dielectric constant to the Poisson-Nernst-Planck model
Sawada, Atsushi
PHYSICAL REVIEW E, 2016, 93 (05)
[27] A conservative finite difference scheme for Poisson-Nernst-Planck equations
Flavell, Allen
Machen, Michael
Eisenberg, Bob
Kabre, Julienne
Liu, Chun
Li, Xiaofan
JOURNAL OF COMPUTATIONAL ELECTRONICS, 2014, 13 (01) : 235 - 249
[28] POISSON-NERNST-PLANCK (PNP) THEORY OF AN OPEN IONIC CHANNEL
EISENBERG, R
CHEN, DP
BIOPHYSICAL JOURNAL, 1993, 64 (02) : A22 - A22
[29] Poisson-Nernst-Planck systems for ion channels with permanent charges
Eisenberg, Bob
Liu, Weishi
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 38 (06) : 1932 - 1966
[30] Exact solution of the Poisson-Nernst-Planck equations in the linear regime
Golovnev, A.
Trimper, S.
JOURNAL OF CHEMICAL PHYSICS, 2009, 131 (11):

← 1 2 3 4 5 →