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Solutions for the microsensor thermistor equations in the small bias case*

Published online by Cambridge University Press:  14 November 2011

W. Allegretto  and
H. Xie
W. Allegretto
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
H. Xie
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
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Synopsis

The behaviour of a microsensor thermistor is described by a system of nonlinear coupled elliptic equations subject to mixed Dirichlet-Neumann boundary conditions, to be solved on different domains. We employ the Implicit Function Theorem in Banach space to show that the system has a solution for small applied bias. It does not appear that earlier approaches for similar thermistor problems can be employed in this physically important situation. The fact that the problem is cast in a subset of R3 is significant in our presentation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 987 - 999
Copyright
Copyright © Royal Society of Edinburgh 1993

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