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The mathematics of the Thomson effect
Author(s):
Giovanni
Cimatti
Journal:
Quart. Appl. Math.
MSC (2000):
Primary 35J60, 35K50, 80A22
Posted:
July 29, 2009
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Abstract:
The paper deals with the elliptic system of the thermistor problem in 3 dimensions taking into account the Thomson effect. Existence and uniqueness results are presented. The proofs are based on a reduction to a two-point problem for an ordinary differential equation.
References:
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- S.N. Antonsev and M. Chipot, The thermistor problem: Existence, smoothness, uniqueness, blow up, SIAM J. Math. Anal. 25 (1994), 67-83. MR 1278895 (95f:35013)
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- G. Cimatti, Existence and Uniqueness for the Equations of the Joule-Thomson Effect, Appl. Anal., 41 (1991), 131-144. MR 1103851 (92f:35135)
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- G. Cimatti, Stability and Multiplicity of Solutions for the Thermistor Problem, Ann. Mat. Pura Appl., 181 (2002), 181-212. MR 1911935 (2003g:35056)
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- H. Diesselhorst, Über das Probleme eines elektrisch erwämtern Leiters, Ann. Phys., 1 (1900), 312-325.
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- S.D. Howison, J.F. Rodrigues and M. Shilor, Stationary solutions for the thermistor problem, J. Math. Appl., 174 (1993), 46-58. MR 1215637 (94h:80005)
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- W. Voigt, Über ein von Herrn Fr. Kohlrausch aufgestelltes Problem der Wärmelehre, Gött. Nachr. 231 (1899), 228-239.
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Additional Information:
Giovanni
Cimatti
Affiliation:
Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, Italy
Email:
cimatti@dm.unipi.it
PII:
S0033-569X-09-01140-6
Keywords:
Thermistor problem,
Thomson effect,
existence and uniqueness results,
multiple solutions
Received by editor(s):
April 3, 2008
Posted:
July 29, 2009
Copyright of article:
Copyright
2009,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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