Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610118 | Journal of Differential Equations | 2015 | 37 Pages |
Abstract
In this work, we examine the stationary one-dimensional classical Poisson-Nernst-Planck (cPNP) model for ionic flow - a singularly perturbed boundary value problem (BVP). For the case of zero permanent charge, we provide a complete answer concerning the existence and uniqueness of the BVP. The analysis relies on a number of ingredients: a geometric singular perturbation framework for a reduction to a singular BVP, a reduction of the singular BVP to a matrix eigenvalue problem, a relation between the matrix eigenvalues and zeros of a meromorphic function, and an application of the Cauchy Argument Principle for identifying zeros of the meromorphic function. Once the zeros of the meromorphic function in a stripe are determined, an explicit solution of the singular BVP is available. It is expected that this work would be useful for studies of other PNP systems.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Weishi Liu, Hongguo Xu,