4 papers
On the existence of a singular limit equation for a model of a self-propelled object motion
Masaharu Nagayama, Koya Sakakibara, Keisuke Takasao
In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn…
The Åojasiewicz-Simon inequality related to grain boundary motion and its applications
Masashi Mizuno, Ayumi Sakiyama, Keisuke Takasao
In this paper, we study the Åojasiewicz-Simon gradient inequality for the mathematical model of grain boundary motion. We first derive a curve shortening equation with time-depend…
Generic mean curvature flow with obstacles
Tim Laux, Keisuke Takasao
We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalize…
Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow
Andrea Chiesa, Keisuke Takasao
In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time…