MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Continuum Limits of Particles Interacting via Diffusion

Nicholas Alikakos, Giorgio Fusco and Georgia Karali


We consider a two phase system mainly in 3 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 quasi static 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 and Otto.

So, the theory of Lifschitz-Slyosov and Wagner is improved by taking into account the geometry of the spatial distribution.

MSC Codes:
ostwald, mullins-sekerka, continuum limits

Related publications

2004 Repository Open Access
Nicholas Alikakos, Giorgio Fusco and Georgia Karali

Continuum limits of particles interacting via diffusion

In: Abstract and applied analysis, 2004 (2004) 3, pp. 215-237