Solutions to a nonlinear Poisson–Nernst–Planck system in an ionic channel |
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Authors: | L Hadjadj K Hamdache D Hamroun |
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Institution: | 1. Faculté des sciences, Université de Blida BP 270 Blida 09000, Algeria;2. CMAP, Ecole Polytechnique, CNRS 91128 Palaiseau Cedex, France;3. AMNEDP, Faculté de mathématiques, USTHB BP 32 El Alia, Algeria |
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Abstract: | A limiting one‐dimensional Poisson–Nernst–Planck (PNP) equations is considered, when the three‐dimensional domain shrinks to a line segment, to describe the flows of positively and negatively charged ions through open ion channel. The new model comprises the usual drift diffusion terms and takes into account for each phase, the bulk velocity defined by (4) including the water bath for ions. The existence of global weak solution to this problem is shown. The proof relies on the use of certain embedding theorem of weighted sobolev spaces together with Hardy inequality. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | Poisson– Nernst– Planck system ion channel unbounded domain weighted spaces |
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