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Poisson–Nernst–Planck Systems for Narrow Tubular-Like Membrane Channels

Poisson–Nernst–Planck Systems for Narrow Tubular-Like Membrane Channels,10.1007/s10884-010-9186-x,Journal of Dynamics and Differential Equations,Weish

Poisson–Nernst–Planck Systems for Narrow Tubular-Like Membrane Channels   (Citations: 2)
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We study global asymptotic behavior of Poisson–Nernst–Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previously studied one-dimensional PNP systems in that it encodes the defining geometry of the three-dimensional membrane channel. To justify this limiting process, we show that the global attractors of the three-dimensional PNP systems are upper semi-continuous as the radius of the channel tends to zero.
Journal: Journal of Dynamics and Differential Equations - J DYN DIFFER EQU , vol. 22, no. 3, pp. 413-437, 2010
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