| Abstract: |
| Hypergraph is a generalization of the usual graph which represents the grouping or connection of multiple members. In order to investigate the structure of network represented by a hypergraph, Prof. Yuichi Yoshida (2022) introduced hypergraph Laplacian, which can be defined as a subdifferential operator of some convex function on a finite dimensional space. In this talk, we first explain the definition and some basic properties of this operator from a viewpoint of the nonlinear evolution equation theory. By using them, we next consider the Cauchy and the time-periodic problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian. |
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