Workshops

Boundary layer solutions of PNP systems

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Workshops

Tai-Chia Lin

2013-10-22
15:30:00 - 16:20:00

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

The Poisson-Nernst-Planck (PNP) system is an important model to describe ion transport in ionic liquids having many applications in biology, chemistry and physics. From the steady state PNP systems, we may derive a new Poisson-Boltzmann type equation called "Charge Conservation Poisson-Boltzmann (CCPB)" equation with a small parameter from the ratio of length scale and dielectric constant. The CCPB equations with Robin boundary conditions may have solutions with boundary layers as the small parameter tends to zero. The profile of boundary layer solutions may represent Debye layers which should have stability observed by physical experiments. Here we provide mathematical results for the stability by studying the linearized problem of PNP systems and proving the linear and nonlinear stability.