WIAS Preprint No. 2607, (2019)

Existence and uniqueness of solution for multidimensional parabolic PDAEs arising in semiconductor modeling


  • Alì, Giuseppe
  • Rotundo, Nella

2010 Mathematics Subject Classification

  • 35K40 35K55 35K51 82D37 94C05


  • Existence and uniqueness of solution, multidimensional parabolic PDAEs, network and semiconductor coupling model




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 multi-dimensional 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.

Appeared in

  • Mathematical Methods in the Applied Sciences, 7 (2021), pp. 6117--6142, DOI 10.1002/mma.7175.

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