A nonlinear partial differential system arising in thermoelectricity
Alfredo Bermúdez, Rafael Muñoz‐Sola, Francisco Pena · European Journal of Applied Mathematics · 2005
In this paper we prove the existence of a solution for a system of nonlinear parabolic partial differential equations arising from thermoelectric modelling of metallurgical electrodes undergoing a phase change. The model consists of an electromagnetic problem for eddy current computation coupled with a Stefan problem for temperature. The proof uses a regularized problem obtained by truncating the source term in temperature equation. Passing to the limit requires fine a priori estimates leading to compactness.