Index-2 elliptic partial differential-algebraic models for circuits and devices

We consider an elliptic partial differential-algebraic model which arises in the modeling of an electric network that contains semiconductor devices. In this context, the electric network is described by linear differential-algebraic equations, while the semiconductor devices are described by nonlinear elliptic partial differential equations. The coupling takes place through the source term for the network equations and the boundary conditions for the device equations. Under the assumption that the fully coupled model has tractability index 2, we prove an existence result for this system. The extension of the notion of tractability index to a specific class of coupled systems is a further result of this paper.