×

Calcul des couches limites dans une membrane porteuse de charges électriques fixes. (French) Zbl 0598.65060

The authors consider the problem of the passage of ions across a membrane. They give a sketch of a proof for an existence theorem for the solution of the differential equations. They refer to previous work on the problem by J. Henry and B. Louro [Analyse asymptotique des équations de l’électrochimie sous l’hypothèse de l’électroneutralité, C. R. Acad. Sci., Paris, Ser. I, 301, No.16, 763-766 (1985)] and poit out that the difficulties associated with singular perturbations may be resolved by the use of ”correctors”. They compare a few experimental results with theoretical results obtained by the collocation method, the ”corrector” method and the continuation method. In some cases order bounds are given but these are not of practical use as the constants cannot be calculated.
Reviewer: Ll.G.Chambers

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
78A35 Motion of charged particles
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] V ASCHER, J CHRISTIANSEN et R D RUSSEL, A Collocation Solverfor Mixed OrderSystems of Boundary Value Problems, Technical Report 77-13 Nov 1977
[2] T REE CHAY et NORMAN, J ZABUSKY, Dual-Mode Potential Oscillations on a Immo-bilized Acetylchohnesterase Membrane System, Journal of Biological Physics Vol 11, 1983
[3] EJ DOEDEL et J P KERNEVEZ, Software for Continuous problems in ordinary differential équations with applications, Technical Report, Applied Mathematics,Cal Inst of Technology, 1985
[4] A FRIBOULET, Excitabilité et instabilités de membranes artificielles porteuses de fonctions biologiques, These, Université de Compiegne, France, 1980
[5] J HENRY et B LOURO, Comptes rendus a l’Academie des Sciences, Tome 301, Série 1, n^\circ 16, p 763, 1985 MR817591
[6] J J LIONS, Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal, Springer-Verlag, Vol 323 Zbl0268.49001 · Zbl 0268.49001
[7] H OSHIMA et S OHKI, Donnan Potential and Surface Potential of a Charged Membrane, Journal of Biophysics, Vol 47, 1985
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.