The convergence to a motion by mean curvature by diffusively scaling a nonlocal evolution equation, describing the macroscopic behavior of a ferromagnetic spin system with Kac interaction and Glauber dynamics has recently been proved. The convergence is proven up to the times when the motion by curvature is regular. Here we show the convergence at all times in the two-dimensional case. Since, in this case, the only singularity is the shrinking to a point of a closed curve, we verify that the curve actually disappears past the singularity. © 1994 Kluwer Academic Publishers.
Motion by mean curvature by scaling a nonlocal equation: Convergence at all times in the two-dimensional case / Butta', Paolo. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 31:1(1994), pp. 41-55. [10.1007/bf00751170]
Motion by mean curvature by scaling a nonlocal equation: Convergence at all times in the two-dimensional case
BUTTA', Paolo
1994
Abstract
The convergence to a motion by mean curvature by diffusively scaling a nonlocal evolution equation, describing the macroscopic behavior of a ferromagnetic spin system with Kac interaction and Glauber dynamics has recently been proved. The convergence is proven up to the times when the motion by curvature is regular. Here we show the convergence at all times in the two-dimensional case. Since, in this case, the only singularity is the shrinking to a point of a closed curve, we verify that the curve actually disappears past the singularity. © 1994 Kluwer Academic Publishers.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.