| Abstract: |
| In this talk, we consider the solvability of a multi-valued nonlinear ODE system obtained by replacing the Laplacian of the Cahn-Hilliard equations with a hypergraph Laplacian. The hypergraph Laplacian is a nonlinear multi-valued operator introduce to analyze complex network structures. In previous studies, it is known that solutions to evolution equations with this operator behave similarly to that of the heat equation. By analogy with the Cahn-Hilliard equations, we can expect that the system we consider represents a multi-phase decomposition in a discrete domain. However, due to the nonlinearity and multi-valuedness of the hypergraph Laplacian, standard methods for the Cahn-Hilliard equations can not be applied. In this talk, we will introduce a new proof method by using properties of the hypergraph Laplacian. |
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