Continuum limits of particles interacting via diffusion. (14th April 2004)

• Record Type: Journal Article
• Authors: Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
• Is Part Of: Abstract and applied analysis. Volume 2004:Number 3(2004)
• Page Start: 215
• Page End: 237
• Publication Date: 2004-04-14
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337504310080
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider a two-phase system mainly in three dimensions and we examine the coarsening of the spatial distribution, driven by the reduction of interface energy and limited by diffusion as described by the quasistatic Stefan free boundary problem. Under the appropriate scaling we pass rigorously to the limit by taking into account the motion of the centers and the deformation of the spherical shape. We distinguish between two different cases and we derive the classical mean-field model and another continuum limit corresponding to critical density which can be related to a continuity equation obtained recently by Niethammer andOtto. So, the theory of Lifshitz, Slyozov, and Wagner is improved by taking into account the geometry of the spatial distribution.