Existence and uniqueness for an elliptic PDAE model of integrated circuits

In refined network analysis, a compact network model is coupled with distributed models for interconnects and semiconductor devices, linking differential-algebraic equations to partial differential equations, thus creating PDAEs. This paper deals with linear RLC networks containing one-dimensional diodes as distributed devices, modeled by the stationary drift-diffusion equations. For the resulting mixed initial boundary value problem we prove a uniqueness result for solutions close to equilibrium, i.e., with small initial data and electrical sources, based on a contraction argument.