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A non-local thermistor problem

Published online by Cambridge University Press:  26 September 2008

W. Allegretto and
H. Xie
W. Allegretto
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
H. Xie
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
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Abstract

We consider the question of the existence/non-existence of solutions for the non-local nonlinear elliptic system which models a thermistor driven by a current source. Specifically, we show that for small input current there exists a solution, while this will not in general be the case for a sufficiently large current. A feature of our estimates is that the conditions for non-existence are determined by local criteria on the domain and the coefficients. Our basic tools for existence involve truncation, L2.μ estimates and fixed point arguments. Non-existence is obtained by averaging procedures and an application of Barta's Inequality.

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Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 1 , February 1995, pp. 83 - 94
Copyright
Copyright © Cambridge University Press 1995

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