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

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Document pages: 26 pages

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 modelderived from the fully nonlinear isothermal Euler gas equations. We formulatean optimal control problem on a given network and introduce a time discretizationthereof. We then study the well-posedness of the correspondingtime-discrete optimal control problem. In order to further reduce the complexity,we consider an instantaneous control strategy. The main part of thepaper is concerned with a non-overlapping domain decomposition of thesemi-linear elliptic optimal control problem on the graph into local problemson a small part of the network, ultimately on a single edge.

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