25 citations · 39 across the 13 of their papers we have counts for
18 papers
Generic Mean Curvature Flow With Rough Weights
Fabius Krämer, Tim Laux, Keisuke Takasao
We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a gene…
Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
Tim Laux, Keisuke Takasao
Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cah…
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 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…
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…
On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition
Katerina Nik, Keisuke Takasao
We study Brakke's mean curvature flow with obstacles and with a right-angle boundary condition. Assuming that the obstacles have -boundaries we prove that a weak solution…
Existence of weak solution to volume preserving mean curvature flow in higher dimensions
Keisuke Takasao
In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of -flow. This flow is al…
Long time behavior for a curvature flow of networks related to grain bundary motion with the effect of lattice misorientations
Takashi Kagaya, Masashi Mizuno, Keisuke Takasao
The mathematical model of grain boundary motion, including lattice misorientations' effect, is considered. When time-dependent lattice misorientations are state variables of the su…
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…
A curve shortening equation with time-dependent mobility related to grain boundary motions
Masashi Mizuno, Keisuke Takasao
A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation p…
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…
Gradient estimates for mean curvature flow with Neumann boundary conditions
Masashi Mizuno, Keisuke Takasao
We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature flow. As an appli…
Existence of weak solution for volume preserving mean curvature flow via phase field method
Keisuke Takasao
We study the phase field method for the volume preserving mean curvature flow. Given an initial hypersurface we proved the existence of the weak solution for the volume prese…
Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow
Keisuke Takasao
In this paper we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constra…
Existence and regularity of mean curvature flow with transport term in higher dimensions
Keisuke Takasao, Yoshihiro Tonegawa
Given an initial hypersurface and a time-dependent vector field in a Sobolev space, we prove a time-global existence of a family of hypersurfaces which start from the given h…