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arXiv · 1902.01505

Optimal control of a thermistor problem with vanishing conductivity

Volodymyr Hrynkiv·Sergiy Koshkin
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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.

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Volodymyr Hrynkiv, Sergiy Koshkin. 2019-02-05. Optimal control of a thermistor problem with vanishing conductivity. https://doi.org/10.1007/s00245-018-9511-z

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