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Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system
Yoshikazu Giga, Ayato Kubo, Hirotoshi Kuroda +3
This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling…
On a singular limit of the Kobayashi--Warren--Carter energy
Yoshikazu Giga, Jun Okamoto, Koya Sakakibara +1
By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the…
A finer singular limit of a single-well Modica--Mortola functional and its applications to the Kobayashi--Warren--Carter energy
Yoshikazu Giga, Jun Okamoto, Masaaki Uesaka
An explicit representation of the Gamma limit of a single-well Modica--Mortola functional is given for one-dimensional space under the graph convergence which is finer than convent…
Short-time approximate solutions of an equation modeling a camphor motion
Jishan Fan, Masaharu Nagayama, Gen Nakamura +1
As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a couple…
A new numerical scheme for constrained total variation flows and its convergence
Yoshikazu Giga, Koya Sakakibara, Kazutoshi Taguchi +1
In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained i…
Carleman estimate and unique continuation for a structured population model
Masaaki Uesaka, Masahiro Yamamoto
We consider a time-dependent structured population model equation and establish a Carleman estimate. We apply the Carleman estimate to prove the unique continuation which means tha…