题 目：Poisson-Nernst-Planck Systems and Ion Channel Problems

报告人：刘为世教授(吉林大学唐敖庆讲座教授,美国堪萨斯大学教授)

时 间：2016年5月24日 上午9:15

地 点：数学楼一楼报告厅

摘 要：The focus of this lecture series is on mathematical analysis of Poisson-Nernst-Planck (PNP) systems as fundamental primitive models for ionic flows (diffusion of charged particles) through nano-scale ion channels. Ion channels are large proteins embedded on cell membrane that provide channels for ions ow between the inside and outside of cells. This is the main way for cells to communicate with each other and with the outside world. Functions of ion channels are thus central to all living organisms.

This research area belongs to general _fields of electrolyte solutions concerning basic theories of chemistry and physics with many specifics from electro-biology (physiology). Due to the natural multi-parameter and multi-scale features, and nonlinear interactions presented in ionic flows, the study of ion channel problems necessarily demands a great deal of mathematical analysis efforts and, most likely, new mathematical theory.

A geometric singular perturbation framework for analyzing PNP is developed by myself and collaborators during past several years based on advanced nonlinear dynamical systems theories of invariant manifolds and modern geometric singular perturbations. For applications of this general framework to PNP type models, special structures are revealed that allow more or less explicit characterizations of critical quantities for ionic flows in terms of physical parameters defining the problem. In turn, concrete information can be extracted to provide direct, hopefully significant, insights for mechanism of critical phenomena of ionic flows.

First lecture consists of three parts:

1. A briefly review of the modern invariant manifold theory

2. A briefly review of a general geometric singular perturbation

theory (GSP)

3. A basis of ion channels and PNP models for ionic flows