Journal
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume 22, Issue 3, Pages 413-437Publisher
SPRINGER
DOI: 10.1007/s10884-010-9186-x
Keywords
Poisson-Nernst-Planck system; Global attractors; Upper semi-continuity
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Funding
- NSF [DMS-0406998, DMS-0807327, DMS-0703521]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0807327] Funding Source: National Science Foundation
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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.
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