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IMA Journal of Mathematical Control and Information Advance Access published online on September 15, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl026
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received September 26, 2005
Accepted August 2, 2006

Article

Optimal control for the thermistor problem with a current limiting device

Giovanni Cimatti 1 *

1 Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, Italy

* To whom correspondence should be addressed.
Giovanni Cimatti, E-mail: cimatti{at}dm.unipi.it


  Abstract

The problem of finding in the thermistor problem the optimal difference of applied potential in order to minimize a suitable cost functional involving the temperature is studied. We find the optimal system in the elementary case of constant electric conductivity. In addition, a theorem of existence of the optimal solution is given in the general case of conductivities depending on the temperature.

Keywords: thermistor problem; optimal control; current limiting device.
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