An electrothermal instability in a conducting wire: Homogeneous and inhomogeneous stationary states for an exactly solvable model

Abstract

An exactly solvable model of the ballast resistor is considered. Analytic expressions are obtained for the nonuniform stationary temperature distributions and the correspondingI–V characteristics. A bifurcation point for Neumann boundary conditions is found and its analytic properties are discussed. It is found that the infinite wire limit plays a role analogous to the thermodynamic limit in statistical mechanics for equilibrium phase transitions.