Solvability for induction hardening including nonlinear magnetic field and controlled Joule heating

Abstract

In this paper, we investigate a mathematical model for the electromagnetic ‘induction heating’ of a continuous medium at rest. We assume that the magnetic induction field is a nonlinear function of the magnetic field and that the electric conductivity is temperature dependent. The coupling between the equations describing electro-magnetic field and the heat equation is provided through the nonlinear function on the one hand and through the Joule heating term on the other hand. We prove the existence of a weak solution to this strongly coupled nonlinear system of Maxwell-heat equations with the truncated quadratic Joule heating term.

Keywords:

• Joule heating
• Maxwell’s equations
• Monotone operators
• Rothe’s method

AMS Subject Classifications:

• 35K61
• 35Q61
• 35Q79
• 65M12

Additional information

Funding

This work was supported by the BOF-project [number 01J04113]; Ghent University, Belgium and the IAP P7/02-project of the Belgian Science Policy.