4 papers
math.AP2022
Heat equation on the hypergraph containing vertices with given data
Takeshi Fukao, Masahiro Ikeda, Shun Uchida
This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or `…
math.AP2021
Nonlinear Evolution Equation Associated with Hypergraph Laplacian
Masahiro Ikeda, Shun Uchida
Let be a finite set, be a set of hyperedges, and be an edge weight. On the (wighted) hypergraph , we can define a mul…
math.AP2020
Periodic Problem for Doubly Nonlinear Evolution Equation
Masahiro Koike, Mitsuharu Ôtani, Shun Uchida
We are concerned with the time-periodic problem of some doubly nonlinear equations governed by differentials of two convex functionals over uniformly convex Banach spaces. Akagi--S…
math.AP2020
Solvability of Doubly Nonlinear Parabolic Equation with -Laplacian
Shun Uchida
In this paper, we consider a doubly nonlinear parabolic equation with the homogeneous Dirichlet boundary condition in a bou…