Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The thermistor problem for conductivity which vanishes at large temperature

Authors: Xinfu Chen and Avner Friedman
Journal: Quart. Appl. Math. 51 (1993), 101-115
MSC: Primary 35R35; Secondary 35J45, 80A20
DOI: https://doi.org/10.1090/qam/1205940
MathSciNet review: MR1205940
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Abstract: The thermistor problem is modeled as a coupled system of nonlinear elliptic equations. When the conductivity coefficient $ \sigma \left( u \right)$ vanishes ($ u$ = temperature) one of the equations becomes degenerate; this situation is considered in the present paper. We establish the existence of a weak solution and, under some special Dirichlet and Neumann boundary conditions, analyze the structure of the set $ \left\{ {\sigma \left( u \right) = 0} \right\}$ and also prove uniqueness.

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DOI: https://doi.org/10.1090/qam/1205940
Article copyright: © Copyright 1993 American Mathematical Society

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