Preprint: Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits
Together with Georg Heinze and Jan-Frederik Pietschmann, we study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on the case where the dynamics are driven by an entropy functional defined both on the metric edges and vertices, we provide a rigorous understanding of such systems of coupled ordinary and partial differential equations as (generalized) gradient flows in continuity equation format.
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