Optimal control of a thermistor problem with vanishing conductivity
arXiv:1902.01505 · doi:10.1007/s00245-018-9511-z
Abstract
An optimal control of a steady state thermistor problem is considered, where the convective boundary coefficient is taken as the control variable. A distinctive feature of this paper is that the problem is considered in arbitrary dimensions, and the electrical conductivity is allowed to vanish above a threshold temperature value. The existence of a steady state is proved, an objective functional is introduced, the existence of the optimal control is proved, and the optimality system is derived.
23 pages, no figures