Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract
Rocca, Elisabetta
We study a model for induction hardening of steel. The related differential system consists of a vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. By similar arguments the linearized state system is discussed, and the adjoint system is investigated. These results allow to derive first-order necessary conditions for the optimal control problem.