Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Existence and uniqueness for a two-point problem with an application to the electrical heating in an electrolyte

Author: Giovanni Cimatti
Journal: Quart. Appl. Math. 70 (2012), 383-392
MSC (2000): Primary 34B15, 35B30
DOI: https://doi.org/10.1090/S0033-569X-2012-01268-0
Published electronically: February 29, 2012
MathSciNet review: 2953109
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a two-point boundary value problem for a first-order nonlinear differential equation depending on a parameter. The results of existence and uniqueness obtained are applied to the determination of the electric potential and temperature in an electrolytic solution contained in a vessel of arbitrary shape.

References [Enhancements On Off] (What's this?)

  • 1. Antonio Ambrosetti and Giovanni Prodi, A primer of nonlinear analysis, Cambridge Studies in Advanced Mathematics, vol. 34, Cambridge University Press, Cambridge, 1993. MR 1225101
  • 2. R. Caccioppoli, Un principio di inversione per le corrispondenze funzionali, Atti Accad. Naz. Lincei, 16, (1932), 392-400.
  • 3. G. Cimatti, Remark on existence, uniqueness and semi-explicit solvability of systems of autonomous partial differential equations in divergence form with constant boundary conditions, to appear in Proc. (A), Roy. Soc. Edinburgh, (2011).
  • 4. P. Lévy, Sur les fonctions de lignes implicites, Bull. Soc. Math. France 48 (1920), 13–27 (French). MR 1504790
  • 5. J. Koryta and J. Dvorak, Principle of Electrochemistry, John Wiley, 1987.
  • 6. L.I. Antropov, Theoretical Electrochemistry, MIR Publishers, Moscow, 1977.
  • 7. M. Planck, Ueber die Erregung von Electricität und Wärme in Electrolyten, Annalen der Physik und Chemie, 39, (1890), 161-186.

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Additional Information

Giovanni Cimatti
Affiliation: Department of Mathematics, Largo Bruno Pontecorvo 5, Pisa, Italy
Email: cimatti@dm.unipi.it

DOI: https://doi.org/10.1090/S0033-569X-2012-01268-0
Received by editor(s): October 20, 2010
Published electronically: February 29, 2012
Article copyright: © Copyright 2012 Brown University

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