Parabolic differential-algebraic multiphysics models in electrical network design

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.
For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.