Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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.


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DOI: https://doi.org/10.1090/qam/1012273
Article copyright: © Copyright 1989 American Mathematical Society


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