Doubly nonlinear equation with perturbation governed by hypergraph Laplacian

Abstract

The hypergraph Laplacian, which was introduced to study the structure of complicated networks in the information science, is defined as a set-valued operator on a finite-dimensional Euclidean space. In previous works, we have shown that a nonlinear ordinary differential equation governed by the hypergraph Laplacian describes the diffusion process on a hypergraph, and its behavior closely resembles the heat equation. In this paper, we consider some generalized doubly nonlinear equation governed by the hypergraph Laplacian in order to deal with various diffusion phenomena on discrete domains.

Keywords

hypergraph Laplacian / nonlinear evolution inclusion / doubly nonlinear equation / set-valued differential equation / subdifferential / solvability

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