A nonlocal formulation for the problem of microwave heating of material with temperature dependent conductivity
Abstract
Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell's equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initialboundary value problem has solutions using the Schauder's fixed point theorem.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.00626
 Bibcode:
 2021arXiv210600626C
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs