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We study a model for induction hardening of steel. The related differentialsystem consists of a time domain vector potential formulation of the Maxwell'sequations coupled with an internal energy balance and an ODE for the volumefraction of {\sl austenite}, the high temperature phase in steel. We firstsolve the initial boundary value problem associated by means of a Schauderfixed point argument coupled with suitable a-priori estimates and regularityresults. Moreover, we prove a stability estimate entailing, in particular,uniqueness of solutions for our Cauchy problem. We conclude with some finiteelement simulations for the coupled system.

Analysis and simulations of multifrequency induction hardening