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