A note on the thermistor problem in two space dimensions
Author:
Sam Howison
Journal:
Quart. Appl. Math. 47 (1989), 509-512
MSC:
Primary 35Q20; Secondary 80A20
DOI:
https://doi.org/10.1090/qam/1012273
MathSciNet review:
MR1012273
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Abstract: We consider two coupled nonlinear p.d.e’s describing heat and current flow in a thermistor. For certain boundary conditions these equations may be reduced to one nonlinear o.d.e. and Laplace’s equation, as noted in [1]. We give a geometrical interpretation of this reduction in two space dimensions in terms of a conformal map from the thermistor onto a rectangle.
- Giovanni Cimatti, Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Quart. Appl. Math. 47 (1989), no. 1, 117–121. MR 987900, DOI https://doi.org/10.1090/S0033-569X-1989-0987900-9
H. Diesselhorst, Über des Probleme eines elektrisch erwärmten Leiters, Ann. Phys. 1, 312–325 (1900)
A. C. Fowler, E. J. Hinch, and S. D. Howison, Temperature surges in thermistors, to appear in Proceedings of ECMI Conference on Mathematics in Industry, Strathclyde, 1988, ed. S. McKee, publ. G. Teubner
G. Cimatti, Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Quart. Appl. Math. 47, 117–121 (1989)
H. Diesselhorst, Über des Probleme eines elektrisch erwärmten Leiters, Ann. Phys. 1, 312–325 (1900)
A. C. Fowler, E. J. Hinch, and S. D. Howison, Temperature surges in thermistors, to appear in Proceedings of ECMI Conference on Mathematics in Industry, Strathclyde, 1988, ed. S. McKee, publ. G. Teubner
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Article copyright:
© Copyright 1989
American Mathematical Society