4 papers
Cahn-Hilliard equation associated with hypergraph
Takeshi Fukao, Masahiro Ikeda, Shun Uchida
A hypergraph Laplacian was introduced to investigate the structure of networks written as hypergraphs. It was shown that the behavior of solutions to an evolution equation associat…
Asymptotic analysis of transmission problems with parameter-dependent Robin conditions
Takeshi Fukao
We study a transmission problem of {N}eumann--{R}obin type involving a parameter and perform an asymptotic analysis with respect to . The limits and …
Optimal control problem of evolution equation governed by hypergraph Laplacian
Takeshi Fukao, Masahiro Ikeda, Shun Uchida
In this paper, we consider an optimal control problem of an ordinary differential inclusion governed by the hypergraph Laplacian, which is defined as a subdifferential of a convex…
Optimal control of gradient flows via the Weighted Energy-Dissipation method
Takeshi Fukao, Ulisse Stefanelli, Riccardo Voso
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gr…