%0 Journal Article
%T Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks
%A G¨šnter Leugering
%J Applied Mathematics
%P 1074-1099
%@ 2152-7393
%D 2017
%I Scientific Research Publishing
%R 10.4236/am.2017.88082
%X 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.
%K Optimal Control
%K Gas Networks
%K EulerĄ¯s Equation
%K Hierarchy of Models
%K Semi-Linear Approximation
%K Non-Overlapping Domain Decomposition
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=78502