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Microwave electromagnetic heating are widely used in many industrialprocesses. The mathematics involved is based on the Maxwell's equations coupledwith the heat equation. The thermal conductivity is strongly dependent on thetemperature, itself an unknown of the system of P.D.E. We propose here a modelwhich simplifies this coupling using a nonlocal term as the source of heating.We prove that the corresponding mathematical initial-boundary value problem hassolutions using the Schauder's fixed point theorem.

A nonlocal formulation for the problem of microwave heating of material with temperature dependent conductivity