Fine structure of the interface motion. (English) Zbl 1008.45008

Buttà, Paolo; De Mási, Anna

Differ. Integral Equ. 12, No. 2, 207-259 (1999).

Summary: We study a non local evolution and define the interface in terms of a local equilibrium condition. We prove that in a diffusive scaling limit the local equilibrium condition propagates in time thus defining an interface evolution which is given by a motion by mean curvature. The analysis extend through all times before the appearance of singularities.

MSC:

45M10	Stability theory for integral equations
82C24	Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
45G10	Other nonlinear integral equations
47J05	Equations involving nonlinear operators (general)

Keywords:

local equilibrium condition; diffusive scaling limit; interface evolution