Limiting current singularities in electro diffusion
Author:
C. Dubi
Journal:
Quart. Appl. Math. 61 (2003), 329-335
MSC:
Primary 34B05; Secondary 34B16, 34B60
DOI:
https://doi.org/10.1090/qam/1976373
MathSciNet review:
MR1976373
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Abstract: This paper concerns the phenomenon of limiting current in the local electro neutrality approximation of electrodiffusion. The limiting current is the value of the control parameter, the electric current, for which the straightforward split of an electrodiffusional system into a quasi-electro-neutral bulk and charged boundary (electric double) layer valid near the equilibrium is no longer expected to stand. Singularities in the solution appearing at the limiting current are studied.
- Isaak Rubinstein, Electro-diffusion of ions, SIAM Studies in Applied Mathematics, vol. 11, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. MR 1075016
- M. Primicerio, I. Rubinstein, and B. Zaltzman, Electrodiffusional free boundary problem, in a bipolar membrane (semiconductor diode), at a reverse bias for constant current, Quart. Appl. Math. 57 (1999), no. 4, 637–659. MR 1724297, DOI https://doi.org/10.1090/qam/1724297
- I. Rubinstein and B. Zaltzman, Electrodiffusional free boundary problem in concentration polarization in electrodialysis, Math. Models Methods Appl. Sci. 6 (1996), no. 5, 623–648. MR 1403724, DOI https://doi.org/10.1142/S0218202596000250
- Fatiha Alabau, Structural properties of the one-dimensional drift-diffusion models for semiconductors, Trans. Amer. Math. Soc. 348 (1996), no. 3, 823–871. MR 1329526, DOI https://doi.org/10.1090/S0002-9947-96-01519-X
I. Rubinstein, Electro diffusion of ions, SIAM, 1990
M. Primicerio, I. Rubinstein, and B. Zaltsman, Electrodiffusional free boundary problem in a bipolar membrane at a reverse bias for constant current, Quart. Appl. Math. 57, 637 (1999)
I. Rubinstein and B. Zaltsman, Electrodiffusional free boundary problem in concentration polarization in electrodialysis, Mathematical Models and Methods in Applied Science 6, 263 (1996)
F. Alabau, Structural properties of the one-dimensional drift diffusion models for semiconductors, Trans. Amer. Math. Soc., 3486 (1996)
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Article copyright:
© Copyright 2003
American Mathematical Society
