Abstract
An optimal control of a steady state thermistor problem is considered where the convective boundary coefficient is taken to be the control variable. A distinct feature of this paper is that the problem is considered in \({\mathbb {R}}^d\), where \(d>2\), and the electrical conductivity is allowed to vanish above a threshold temperature value. Existence of the state system is proved. An objective functional is introduced, existence of the optimal control is proved, and the optimality system is derived.
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Hrynkiv, V., Koshkin, S. Optimal Control of a Thermistor Problem with Vanishing Conductivity. Appl Math Optim 81, 563–590 (2020). https://doi.org/10.1007/s00245-018-9511-z
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DOI: https://doi.org/10.1007/s00245-018-9511-z