Optimal control for the thermistor problem with a current limiting device

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 optimaldifference of applied potential in order to minimize a suitablecost functional involving the temperature is studied. We findthe optimal system in the elementary case of constant electricconductivity. In addition, a theorem of existence of the optimalsolution is given in the general case of conductivities dependingon the temperature.