2020
DOI: 10.48550/arxiv.2007.10271
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Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation

Abstract: We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the network nodes, and its movement throughout the network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE)… Show more

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