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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the existence of multiple steady-state solutions in the theory of electrodiffusion.
Part I: the nonelectroneutral case.
Part II: a constructive method for the electroneutral case


Author: Fatiha Alabau
Journal: Trans. Amer. Math. Soc. 350 (1998), 4709-4756
MSC (1991): Primary 35G30, 35J25, 35B50
MathSciNet review: 1616008
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Abstract: We give a constructive method for giving examples of doping functions and geometry of the device for which the nonelectroneutral voltage driven equations have multiple solutions. We show in particular, by performing a singular perturbation analysis of the current driven equations that if the electroneutral voltage driven equations have multiple solutions then the nonelectroneutral voltage driven equations have multiple solutions for sufficiently small normed Debye length. We then give a constructive method for giving examples of data for which the electroneutral voltage driven equations have multiple solutions.


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Additional Information

Fatiha Alabau
Affiliation: I.R.M.A., Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex (France)
Email: alabau@math.u-strasbg.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02334-4
PII: S 0002-9947(98)02334-4
Received by editor(s): November 30, 1995
Article copyright: © Copyright 1998 American Mathematical Society