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
Full-text PDF Free Access
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
- Antonio Ambrosetti and Giovanni Prodi, A primer of nonlinear analysis, Cambridge Studies in Advanced Mathematics, vol. 34, Cambridge University Press, Cambridge, 1993. MR 1225101
- R. Caccioppoli, Un principio di inversione per le corrispondenze funzionali, Atti Accad. Naz. Lincei, 16, (1932), 392-400.
- 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).
- P. Lévy, Sur les fonctions de lignes implicites, Bull. Soc. Math. France 48 (1920), 13–27 (French). MR 1504790
- J. Koryta and J. Dvorak, Principle of Electrochemistry, John Wiley, 1987.
- L.I. Antropov, Theoretical Electrochemistry, MIR Publishers, Moscow, 1977.
- M. Planck, Ueber die Erregung von Electricität und Wärme in Electrolyten, Annalen der Physik und Chemie, 39, (1890), 161-186.
References
- A. Ambrosetti and G. Prodi, Nonlinear Analysis, Cambridge University Press, Cambridge, 1993. MR 1225101 (94f:58016)
- R. Caccioppoli, Un principio di inversione per le corrispondenze funzionali, Atti Accad. Naz. Lincei, 16, (1932), 392-400.
- 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).
- P. Levy, Sur les fonctions de lignes implicites, Bull. Soc. Math. Fr., 48, (1920), 13-27. MR 1504790
- J. Koryta and J. Dvorak, Principle of Electrochemistry, John Wiley, 1987.
- L.I. Antropov, Theoretical Electrochemistry, MIR Publishers, Moscow, 1977.
- M. Planck, Ueber die Erregung von Electricität und Wärme in Electrolyten, Annalen der Physik und Chemie, 39, (1890), 161-186.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
34B15,
35B30
Retrieve articles in all journals
with MSC (2000):
34B15,
35B30
Additional Information
Giovanni Cimatti
Affiliation:
Department of Mathematics, Largo Bruno Pontecorvo 5, Pisa, Italy
Email:
cimatti@dm.unipi.it
Received by editor(s):
October 20, 2010
Published electronically:
February 29, 2012
Article copyright:
© Copyright 2012
Brown University
