33 citations · 33 across the 6 of their papers we have counts for
6 papers
Stability of the critical constant steady state of a Keller--Segel model
Nobuhito Miyake, Hiroshi Wakui, Tetsuya Yamada
In this paper, we prove the asymptotic stability of the critical constant steady state for a simplified parabolic--elliptic Keller--Segel system in (), whic…
Initial traces and solvability of the fast diffusion equation with power-type nonlinearity
Kazuhiro Ishige, Nobuhito Miyake
We investigate the qualitative behavior of the initial traces of nonnegative solutions to the fast diffusion equation with power-type nonlinearity. Necessary conditions for the exi…
Initial traces and solvability of porous medium equation with power nonlinearity
Kazuhiro Ishige, Nobuhito Miyake, Ryuichi Sato
In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existenc…
A thresholding algorithm to Willmore-type flows via fourth order linear parabolic equation
Katsuyuki Ishii, Yoshihito Kohsaka, Nobuhito Miyake +1
We propose a thresholding algorithm to Willmore-type flows in . This algorithm is constructed based on the asymptotic expansion of the solution to the initial value p…
Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations
Hans-Christoph Grunau, Nobuhito Miyake, Shinya Okabe
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic pr…
The homogenization method for topology optimization of structures: old and new
Grégoire Allaire, Lorenzo Cavallina, Nobuhito Miyake +2
These are the lecture notes of a short course on the homogenization method for topology optimization of structures, given by Grégoire Allaire, during the "GSIS International Summer…