7 papers · 1 filter
The Łojasiewicz-Simon inequality related to grain boundary motion and its applications
Masashi Mizuno, Ayumi Sakiyama, Keisuke Takasao
In this paper, we study the Łojasiewicz-Simon gradient inequality for the mathematical model of grain boundary motion. We first derive a curve shortening equation with time-depende…
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…
On obstacle problem for Brakke's mean curvature flow
Keisuke Takasao
We consider the obstacle problem of the weak solution for the mean curvature flow, in the sense of Brakke's mean curvature flow. We prove the global existence of the weak solution…
Existence of weak solution for mean curvature flow with transport term and forcing term
Keisuke Takasao
We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean…
A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions
Yoshikazu Giga, Fumihiko Onoue, Keisuke Takasao
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a…
Convergence of Landau-Lifshitz equation to multi-phase Brakke's mean curvature flow
Keisuke Takasao
We study the convergence of the system of the Allen-Cahn equations to the weak solution for the multi-phase mean curvature flow in the sense of Brakke. The Landau-Lifshitz equation…