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.

中文翻译：

---

电导消失的热敏电阻问题的最优控制

考虑以对流边界系数为控制变量的稳态热敏电阻问题的最佳控制。本文的一个显着特征是在\（{\ mathbb {R}} ^ d \）中考虑了该问题，其中\（d> 2 \），并且允许电导率在阈值温度以上消失。证明了状态系统的存在。介绍了目标函数，证明了最优控制的存在，并推导了最优系统。