| Partial differential-algebraic equations are the development of differential-algebraicequations, which have more mature theory. As the importance in practical applications,for example, in the integrated electric network circuit model containing semicondunctordevices, many researchers are attracted to study these systems and they have got manyuseful results.In this paper, we consider existence, uniqueness and asymptotic behavior of solutionto a parabolic-elliptic partial differential-algebraic model in electrical network design.Usually, the electrical network is divided into two parts: the lumped model and thedistributed model. In the lumped model, a set of differential-algebraic equations areconsiderered, we used the concepts of topological conditions and perturbation index.In distributed model, we construct a coupling model of parabolic and elliptic partialdifferential-algebraic equations. For the mixed partial differential-algebraic equations,the existence and uniqueness and asymptotic behavior are given. In the first chapter,an introduction of electric network model containing semicondunctor devices is given.Based on the analysis of the relevant references, we introduce our problem for a partialdifferential-algebraic systems. In the second chapter, we describe the modeling of theelectric network. In the third chapter, it is devoted to the existence, uniqueness andasymptotic behavior of solution to partial differential-algebraic coupled system. |
