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100 1 _ |a Fazeny, Ariane
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245 _ _ |a Optimal transport on gas networks
260 _ _ |a Cambridge
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500 _ _ |a Has already been accepted by the European Journal of Applied Mathematics, L:MBVolume and Pages not clear yet
520 _ _ |a Optimal transport tasks naturally arise in gas networks, which include a variety of constraints such as physical plausibility of the transport and the avoidance of extreme pressure fluctuations. To define feasible optimal transport plans, we utilize a p-Wasserstein metric and similar dynamic formulations minimizing the kinetic energy necessary for moving gas through the network, which we combine with suitable versions of Kirchhoff’s law as coupling condition at the nodes. In contrast to existing literature, we especially focus on the non-standard case p=2 to derive an overdamped isothermal model for gases through p-Wasserstein gradient flows in order to uncover and analyze underlying dynamics. We introduce different options for modeling the gas network as an oriented graph including the possibility to store gas at interior vertices and to put in or take out gas at boundary vertices.
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700 1 _ |a Burger, Martin
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700 1 _ |a Pietschmann, Jan-Frederik
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770 _ _ |a Evolution Equations on Graphs: Analysis and Applications
773 _ _ |a 10.1017/S0956792525000051
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