Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4637783 | Journal of Computational and Applied Mathematics | 2017 | 15 Pages |
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
Authors
Jaroslav Chovan, Marián Slodička,