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Chiun-Chang Lee

2011-10-28
13:30:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Understanding ionic transport in the cells plays crucial role in maintaining the physiological function of our bodies. An interesting problem, how is the influence of ionic concentrations on the membrane potential when ions go through ion channels? For this purpose, we derive a new Poisson-Boltzmann (PB_n) equation governing the ionic transport in the ionic channels of the membrane. The PB_n equation has a small parameter ε>0 ( related to the dielectric constant of the cell membrane) and the non-local non- linearity which takes into consideration the preservation of the total amount of each individual ion. In this seminar, we will study the asymptotic behaviour of the solution of the PB_n equation as ε goes to zero. This will provide a viewpoint to see how ion concentrations affect the membrane potential.