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.
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页码：12 / 24
页数：13
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