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A nonlinear partial differential system arising in thermoelectricity

Published online by Cambridge University Press:  14 July 2005

A. BERMÚDEZ
Affiliation:
Depto. de Matemática Aplicada, Univ. de Santiago de Compostela, 15782 Santiago de Compostela, Spain email: mabermud@usc.es
R. MUÑOZ-SOLA
Affiliation:
Depto. de Matemática Aplicada, Univ. de Santiago de Compostela, 15782 Santiago de Compostela, Spain email: mabermud@usc.es
F. PENA
Affiliation:
Depto. de Matemática Aplicada, Univ. de Santiago de Compostela, 15782 Santiago de Compostela, Spain email: mabermud@usc.es

Abstract

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.

Type
Papers
Copyright
2005 Cambridge University Press

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