The paper studies a problem of an optimal control in coefficients for the system of two coupled elliptic equations also known as thermistor problem which provides a simultaneous description of the electric field u= u(x) and temperature θ(x). The coefficient b of operator div(b(x)∇θ(x)) is used as the control in W1,q(Ω) with q> N. The optimal control problem is to minimize the discrepancy between a given distribution θd∈ L1(Ω) and the temperature of thermistor θ∈W01,γ(Ω) by choosing an appropriate anisotropic heat conductivity b(x). Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.
An Indirect Approach to the Existence of Quasi-optimal Controls in Coefficients for Multi-dimensional Thermistor Problem / D'Apice, C.; De Maio, U.; Kogut, P. I.. - (2021), pp. 489-522. [10.1007/978-3-030-50302-4_24]
An Indirect Approach to the Existence of Quasi-optimal Controls in Coefficients for Multi-dimensional Thermistor Problem
De Maio U.;
2021
Abstract
The paper studies a problem of an optimal control in coefficients for the system of two coupled elliptic equations also known as thermistor problem which provides a simultaneous description of the electric field u= u(x) and temperature θ(x). The coefficient b of operator div(b(x)∇θ(x)) is used as the control in W1,q(Ω) with q> N. The optimal control problem is to minimize the discrepancy between a given distribution θd∈ L1(Ω) and the temperature of thermistor θ∈W01,γ(Ω) by choosing an appropriate anisotropic heat conductivity b(x). Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
