Poisson-Nernst-Planck Systems for Narrow Tubular-Like Membrane Channels

被引：74

作者：

Liu, Weishi ^{[1
]}

Wang, Bixiang ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2010年 / 22卷 / 03期

基金：

美国国家科学基金会;

关键词：

Poisson-Nernst-Planck system; Global attractors; Upper semi-continuity; QUALITATIVE PROPERTIES; SEMICONDUCTOR THEORY; BASIC EQUATIONS; TIME BEHAVIOR; THIN DOMAINS; ION CHANNELS; DIFFUSION; PERTURBATION; BOUNDEDNESS; TRANSPORT;

D O I：

10.1007/s10884-010-9186-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study global asymptotic behavior of Poisson-Nernst-Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previously studied one-dimensional PNP systems in that it encodes the defining geometry of the three-dimensional membrane channel. To justify this limiting process, we show that the global attractors of the three-dimensional PNP systems are upper semi-continuous as the radius of the channel tends to zero.

引用

页码：413 / 437

页数：25

共 25 条

[1] Ion flow through narrow membrane channels: part II [J].