Multiscale limits on metric graphs via EDP convergence
A talk in the Oberseminar Analysis series by
Andre from Schlichting
| Abstract: | We consider gradient flows on metric graphs, where mass can evolve between vertices and edges as well as along metric edges. In this way, our model is an extension of the gradient flow formulations by [Erbar, Forkert, Maas, Mugnolo: 10.3934/nhm.2022023] and [Burger, Humpert, Pietschmann: 10.1051/cocv/2023027]. In addition, we consider different scaling regimes leading asymptotically to gradient flows either on the metric edges only (the case considered in the previous works) or the combinatorial graph (vertices only), which can be seen as a Markov chain on finite state space.
We link the scaling regimes by EDP convergence/variational Gamma convergence results and identify different limiting gradient structures for the Markov chain dynamic.
Joint work with Georg Heinze (WIAS Berlin) and Jan-Frederik Pietschmann (U Augsburg). Zoom Meeting ID: [684 0498 9843] Passcode: [241051 $\href{https://uni-bielefeld.zoom-x.de/j/68404989843?pwd=cWNqT3FFZWFxMW1RQ3FvUkZ0MG9Jdz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A8 |