6 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…
Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces
Naoya Hatano, Masahiro Ikeda
In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--Hénon parabolic equation, which is a semilinear heat equation with a power-type…
Stability of standing waves for all frequencies to nonlinear Schrödinger equations with potentials in one dimension
Noriyoshi Fukaya, Masahiro Ikeda, Hiroaki Kikuchi
In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schrödinger equations with potentials. We show that the standing waves are orbitally s…
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…
Boundedness of composition operators from Lorentz spaces to Orlicz spaces
Naoya Hatano, Masahiro Ikeda, Ryota Kawasumi
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study,…
Smoothing estimate for the heat semigroup with a homogeneous weight on Morrey spaces
Naoya Hatano, Masahiro Ikeda
We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the Hardy-Hénon parabolic equation on Morrey spaces. This result is improvement of…