We consider a quasi-one-dimensional Poisson-Nernst-Planck system focusing on internal dynamics of ionic flows through membrane channels. The dynamical system framework is based on geometric singular perturbation theory, from which the existence and uniqueness result can be established. This further allows one to obtain explicit expressions of the approximation of individual fluxes, from which detailed internal dynamics can be described. Effects from different system parameters are examined, interesting and non-intuitive results are obtained, which is critical to further understand the mechanisms of ionic flows through membrane channels.

张明吉, 美国新墨西哥矿业理工学院数学系教授，博士生导师。2013年毕业于美国堪萨斯大学，获理学博士学位；2013-2015年跟随著名数学家 Peter W. Bates在密歇根州立大学做博士后研究。研究方向为非线性动力系统，微分方程及其应用，特别是在离子通道问题(Ion Channel Problem)和发展生物学(developmental biology)中的应用。研究的主要工具是在非线性动力系统不变流形理论上发展起来的几何奇异摄动理论。在研究离子通道问题上，特别是对离子流的动力学行为的研究，做出了重要贡献，得到同行专家学者的高度认可。已在J. Differential Equations、J. Nonlinear Science、Nonlinearity、J. Dynamics and Differential Equations、SIAM J. Applied Mathematics、SIAM J. Applied Dynamical Systems、Advances in Computational Mathematics、Nonlinear Analysis、Discrete and Continuous Dynamical Systems-A等国际著名期刊发表论文近60篇。美国《数学评论》评论员，德国《数学文摘》评论员，担任SIAM J. Applied Mathematics，Discrete and Continuous Dynamical System-A，Int. J. System Science，Fluids，Entropy等近60个SCI杂志特邀审稿人。