4 citations · 5 across the 4 of their papers we have counts for
4 papers
Convergence of the Allen-Cahn equation with transport term in a bounded domain
Yuki Tsukamoto
We study the Allen-Cahn equation with respect to a transport term in a bounded domain. We prove that the limit interface is the mean curvature flow with the transport term, given t…
Prescribed mean curvature equation on torus
Yuki Tsukamoto
Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the -dimensional torus ,…
The Dirichlet problem for a prescribed mean curvature equation
Yuki Tsukamoto
We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the prob…
A diffused interface with the advection term in a Sobolev space
Yoshihiro Tonegawa, Yuki Tsukamoto
We study the asymptotic limit of diffused surface energy in the van der Waals--Cahn--Hillard theory when an advection term is added and the energy is uniformly bounded. We prove th…