The thermistor problem with degenerate thermal conductivity and metallic conduction

María Teresa González Montesinos; Francisco Ortegón Gallego

doi:10.3934/proc.2007.2007.446

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2007, Volume 2007: 446-455. Doi: 10.3934/proc.2007.2007.446 open access

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The thermistor problem with degenerate thermal conductivity and metallic conduction

1.
Departmento de Matemáticas, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, 11002 Cádiz
2.
Departamento de Matemáticas, Universidad de Cádiz, CASEM, Campus del Río San Pedro, 11510 Puerto Real, Cádiz

Received: August 31, 2006

Revised: February 28, 2007

Published: August 2007

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Abstract

The aim of this work is to establish the existence of a capacity solution to the thermistor problem supposing that the thermal and the electrical conductivities are not bounded below by a positive constant value. Furthermore, the thermal conductivity vanishes at points where the temperature is null. These assumptions on data include the case of practical interest of the Wiedemann–Franz law with metallic conduction and lead us to very complex mathematical situations.

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Mathematics Subject Classification: Primary: 35M10, 35J60, 35K65; Secondary: 35J70.

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