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IMA Journal of Mathematical Control and Information Advance Access originally published online on September 15, 2006
IMA Journal of Mathematical Control and Information 2007 24(3):339-345; 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.

Optimal control for the thermistor problem with a current limiting device

Giovanni Cimatti{dagger}

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

{dagger} Email: cimatti{at}dm.unipi.it

Received on September 26, 2005; Accepted on August 2, 2006

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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