Existence of solutions for a model of microwave heating

This paper is concerned with a system of differential equations related to a
circuit model for microwave heating, complemented by suitable initial and
boundary conditions. A RCL circuit with a thermistor is representing the
microwave heating process with temperature-induced modulations on the electric
field. The unknowns of the PDE system are the absolute temperature in the body,
the voltage across the capacitor and the electrostatic potential. Using
techniques based on monotonicity arguments and sharp estimates, we can prove
the existence of a weak solution to the initial-boundary value problem.