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We consider a class of nonlinear partial-differential-algebraic equations, where the nonlinearity is present only in the PDEs and in the coupling conditions, and some additional structural conditions hold. For this special class of PDAEs, we introduce and characterize simple algebraic conditions which lead to a notion of extended tractability index, and exemplify its application to coupled systems arising from microelectronics. [ABSTRACT FROM AUTHOR]

Abstract: The limit of the vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler–Poisson equations with periodic boundary conditions is proved. The equations consist of the balance laws for the electron density and current density for a given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the limit velocity satisfies the incompressible Euler equations with damping. The difference to the zero-Mach-number limit comes from the electrostatic potential which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higher-order energy estimates and a careful use of the Poisson equation. [Copyright &y& Elsevier]

Abstract: In integrated circuit modeling, a general framework is presented for an RCL electric network with a detailed description of the semiconductor devices contained in it. The network part is described by modified nodal analysis, which leads to a system of differential-algebraic equations. The semiconductor devices are described by distributed models, namely, generic systems of partial differential equations with some key features common to all semiconductor models. The network part and the device part are coupled by means of applied potential and electric currents at the contacts of the devices. To take into account devices with more than two contacts, a multigraph description is used for the branches with devices. [Copyright &y& Elsevier]

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multidimensional approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with parabolic-elliptic boundary value problems modeling the diodes. For this mixed initial boundary value problem of partial differential-algebraic equations a first existence and uniqueness result is given, and its asymptotic behavior is discussed. [ABSTRACT FROM AUTHOR]