Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2013-11

Global unique solvability for a quasi-stationary water network model.


Lennart Jansen, Jonas Pade


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2013-11


MSC 2000:

  • 34A09 Implicit equations, differential-algebraic equations
  • 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract This paper analyzes a water pipe network model. In contrast to works existing so far, the underlying model equation for the pipe flow is not stationary but quasi-stationary. In exchange, the model is kept simple in terms of considered control devices. The model gives rise to a differential-algebraic equation (DAE), for which an index analysis, a decoupling and a proof of global unique solvability is established. Two important concepts to analyze DAEs are the Tractability Index and the Strangeness Index. In this paper, we make use of the mixed Tractability-Strangeness Index (TSI). It allows for a topological decoupling of the model DAE.