Poisson-Nernst-Planck Systems and Ion Channel Problems

Electrodiffusion – migration of charges in solutions (typically wa- ter) – is an extremely important process for science and technology. Bulk properties (those are not sensitive to boundary conditions) of ionic mixtures are a central topic of electrochemistry, and has been well studied based on the Poisson-Boltzmann theory back to 1920s documented by the Gouy-Chapmann theory and Debye-Hu ̈ckel theory as well as their improvements. Ion channel problems concern macro- scopic properties of ionic flow through nano-scale membrane channels with more specifics structures and with highly non-trivial boundary ef- fects (in fact, these physical quantities are nonlinear interacting with each other to affect the properties of channel functions). It is not surprising that ion channel problems exhibit more richer phenomena and, on the other hand, are much more challenging than studies of bulk property of ionic mixture. We will start with a short background of ion channels and a brief description of a primitive models – the Poisson-Nernst-Planck system – for ionic flow through ion channels. We then focus on a discussion of a general geometric singular perturbation framework together with special intrinsic structures of PNP systems for an analysis. More im- portantly, we will report a number of concrete results that are directly relevant to central topics of ion channel problems.

举办单位：数学与统计学院

发 布 人：科研助理 发布时间： 2017-07-11

发 布 人：科研助理 发布时间： 2017-07-11

刘为世，美国University of Kansas数学系教授。1985年于吉林大学获学士学位，1997年于Georgia Institute of Technology获博士学位；1997-1999年在University of Missouri-Columbia任访问助理教授，1999-2004年在University of Kansas任助理教授、2004-2009年任副教授、2009年至今任正教授。主要研究方向为Nonlinear dynamics, Center manifold theory for general invariant sets，Geometric singular perturbation theory for turning points， Electrodiusion and ion channel problems等。代表性论文发表在《J. Dynam. Differential Equations》《J. Diff. Equations》《SIAM J. Appl. Dyn. Syst.》《SIAM J. Appl. Math.》《Commun. Math. Sci.》等著名数学杂志上。