Article ID Journal Published Year Pages File Type
4637783 Journal of Computational and Applied Mathematics 2017 15 Pages PDF
Abstract

We study a coupled system of Maxwell’s equations with nonlinear heat equation. We start with derivation of a mathematical model assuming a nonlinear dependency of magnetic field H on magnetic induction B. Moreover the electric conductivity σσ is supposed to be temperature reliant. The coupling between the thermal and electromagnetic equations is provided via the Joule heating term and σσ. Next we use time discretization based on the Rothe’s method to provide energy estimates for discretized system. We prove the existence of a weak solution {u,B} to this coupled system with controlled Joule heating term.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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