Existence and uniqueness of solution for multidimensional parabolic partial differential-algebraic equations arising in semiconductor modeling

This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with multidimensional parabolic-elliptic boundary value problems for the devices. We prove an existence and uniqueness result and the asymptotic behavior of this mixed initial boundary value problem of partial differential-algebraic equations.