Existence and uniqueness of solution for multidimensional parabolic partial differential‐algebraic equations arising in semiconductor modeling. (21st January 2021)

• Record Type: Journal Article
• Authors: Alì, Giuseppe; Rotundo, Nella
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 7(2021)
• Page Start: 6117
• Page End: 6142
• Publication Date: 2021-01-21
• Subjects: existence and uniqueness of solution -- multidimensional parabolic PDAEs -- network and semiconductor coupling model; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7175
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.