Optimal Control of a Thermistor Problem with Vanishing Conductivity

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.

Existence result of the global attractor for a triply nonlinear thermistor problem

“…The thermistor was discovered by Michael Faraday in 1833, who noticed that the temperature increases when the silver sulfides resistance decreases. A lot of studies of the thermistor problem can be found in [1,9,10,14,16].…”

Regularity Results for a Nonlinear Elliptic-Parabolic System with Oscillating Coefficients

“…Modeling and numerical simulations were investigated in [2,13,19]. For optimal control issues, we refer the reader to [12] and the references therein. Also see [1] and its references for obstacle thermistor problems.…”