题目：Singular Perturbation Solutions of Steady State Poisson-Nernst-Planck Systems

报告人：汪翔升 教授 (University of Louisiana at Lafayette, USA)

时间：12月16日（星期五），下午3:00-4:00

地点：致远楼102室

汪翔升，美国University of Louisiana at Lafayette大学助理教授，主要研究渐进分析、微分方程、动力系统和生物数学。迄今为止已在Journal of Differential Equations、Journal of Dynamics and Differential Equations、Journal of Theoretical Biology、Physics Review E、Statistica Sinica等国际期刊上发表学术论文近三十篇。

报告摘要

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and

uniqueness for the three-ion case.

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