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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Blvd., Lawrence, KS, 66045-7594, USA

    Weishi Liu

  2. Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA

    Bixiang Wang

Authors
  1. Weishi Liu
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  2. Bixiang Wang
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Correspondence to Weishi Liu.

Additional information

Dedicated to Professor Jack K. Hale on the occasion of his 80th birthday.

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Liu, W., Wang, B. Poisson–Nernst–Planck Systems for Narrow Tubular-Like Membrane Channels. J Dyn Diff Equat 22, 413–437 (2010). https://doi.org/10.1007/s10884-010-9186-x

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  • DOI: https://doi.org/10.1007/s10884-010-9186-x

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