Roubicek, T. (2013) Nonlinear Partial Differential Equations with Applications (Volume 153 of International Series of Numerical Mathematics). 2nd Edition, Birkh?user-Basel, Basel. https://doi.org/10.1007/978-3-0348-0513-1

has been cited by the following article:

• TITLE: Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

  AUTHORS: Günter Leugering

  KEYWORDS: Optimal Control, Gas Networks, Euler’s Equation, Hierarchy of Models, Semi-Linear Approximation, Non-Overlapping Domain Decomposition

  JOURNAL NAME: Applied Mathematics, Vol.8 No.8, August 17, 2017

  ABSTRACT: We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.