Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks
Günter R. Leugering · Applied Mathematics · 2017
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.