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Title: Approximation and Comparison for Motion by Mean Curvature with Intersection Points
Authors: Bao, W. 
Keywords: Allen-Cahn equation
Intersection point
Kac potential
Motion by mean curvature
Nonlocal evolution equation
Issue Date: Oct-2003
Citation: Bao, W. (2003-10). Approximation and Comparison for Motion by Mean Curvature with Intersection Points. Computers and Mathematics with Applications 46 (8-9) : 1211-1228. ScholarBank@NUS Repository.
Abstract: Consider the motion of a curve in the plane under its mean curvature. It is a very interesting problem to investigate what happens when there are intersection points on the curve at which the mean curvature is singular. In this paper, we study this issue numerically by solving the Allen-Cahn equation and the nonlocal evolution equation with Kac potential. The Allen-Cahn equation is discretized by a monotone scheme, and the nonlocal evolution equation with Kac potential is discretized by the spectral method. Several curves with intersection points under motion by mean curvature are studied. From a simple analysis and our numerical results, we find that which direction to split of the curve at the intersection point depends on the angle of the curve at the point, i.e., it splits in horizontal direction when the angle α > π/2, in vertical direction when α < π/2, and in either direction when α. = π/2. © 2003 Elsevier Ltd. All rights reserved.
Source Title: Computers and Mathematics with Applications
ISSN: 08981221
DOI: 10.1016/S0898-1221(03)90213-6
Appears in Collections:Staff Publications

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