The thermistor problem with degenerate thermal conductivity and metallic conduction

Pages: 446 - 455, Issue Special, September 2007

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María Teresa González Montesinos - Departmento de Matemáticas, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, 11002 Cádiz, Spain (email)
Francisco Ortegón Gallego - Departamento de Matemáticas, Universidad de Cádiz, CASEM, Campus del Río San Pedro, 11510 Puerto Real, Cádiz, Spain (email)

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.

Keywords:  Thermistor problem, Wiedemann–Franz law, metallic conduction, capacity solutions, nonlinear elliptic equations, nonlinear parabolic equations, weak solutions.
Mathematics Subject Classification:  Primary: 35M10, 35J60, 35K65; Secondary: 35J70.

Received: September 2006;      Revised: March 2007;      Published: September 2007.