The thermistor problem with degenerate thermal conductivity and metallic conduction

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.