Existence of weak solution for volume preserving mean curvature flow via phase field method
نویسندگان
چکیده
منابع مشابه
Existence of Weak Solution for Volume Preserving Mean Curvature Flow via Phase Field Method
Abstract. We study the phase field method for the volume preserving mean curvature flow. Given an initial data which is a measure-theoretic boundary of a Caccioppoli set with a suitable density bound, we prove the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula for the re...
متن کاملPhase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the AllenCahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn...
متن کاملMotion by volume preserving mean curvature flow near cylinders
We investigate the volume preserving mean curvature flow with Neumann boundary condition for hypersurfaces that are graphs over a cylinder. Through a center manifold analysis we find that initial hypersurfaces sufficiently close to a cylinder of large enough radius, have a flow that exists for all time and converges exponentially fast to a cylinder. In particular, we show that there exist globa...
متن کاملThe Volume Preserving Mean Curvature Flow near Spheres
By means of a center manifold analysis we investigate the averaged mean curvature flow near spheres. In particular, we show that there exist global solutions to this flow starting from non-convex initial hypersurfaces.
متن کاملA modified phase field approximation for mean curvature flow with conservation of the volume
This paper is concerned with the motion of a time dependent hypersurface ∂Ω(t) in R that evolves with a normal velocity Vn = κ− ∂Ω(t) κ dσ, where κ is the mean curvature of ∂Ω(t), and I stands for 1 |I| I . Phase field approximation of this motion leads to the nonlocal Allen–Cahn equation ∂tu = ∆u− 1 ǫ2 W (u) + 1 ǫ2 Q W (u) dx, where Q is an open box of R containing ∂Ω(t) for all t. We propose ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2017
ISSN: 0022-2518
DOI: 10.1512/iumj.2017.66.6183