Abstract
In this paper, we consider an unsteady thermistor system, where the usual Ohm law is replaced by a non-linear monotone constitutive relation between current and electric field. This relation is modeled by a p-Laplacian type equation for the electrostatic potential ϕ. We prove the existence of weak solutions of this system of PDEs under mixed boundary conditions for ϕ, and a Robin boundary condition and an initial condition for the temperature u.
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