Ostwald ripening in two dimensions -- the rigorous derivation of the equations from the Mullins-Sekerka dynamics
type: Item
instance of: scholarly article
title: Ostwald ripening in two dimensions -- the rigorous derivation of the equations from the Mullins-Sekerka dynamics
zbMATH Open document ID: 1076.35136
author: Nicholas D. Alikakos
author: Georgia Karali
author: Giorgio Fusco
published in: Journal of Differential Equations
publication date: 2004-11-22T00:00:00Z
review text: The authors consider Mullins-Sekerka problem \[ -\Delta\;u=0\quad \text{in }\Omega\setminus\Gamma(t),\quad \frac{\partial u}{\partial \nu}=0\quad\text{on }\partial\Omega,\tag{1} \] \[ u=H,\quad V=\left[\left[\frac{\partial u}{\partial n}\right]\right]\quad \text{on }\Gamma(t), \] where \(H\) is the mean curvature of \(\Gamma(t)\), \(\nu\) is the outward normal to \(\partial \Omega\), \(V\) is the normal velocity of free boundary, \(\left[\left[\frac{\partial u}{\partial n}\right]\right]\) is the jump of derivative to \(\Gamma(t)\). Under the hypothesis that \(\Gamma(0)=\cup_{n=1}^{N}\Gamma_i(0)\) and ``a particle'' \(\Gamma_i(0)\) is a small perturbation of a circle with a small radius, the authors prove the existence of global weak and classical solution to (1) and investigate asymptotic behaviour of particles.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 2117236
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: stability
zbMATH Keywords: existence of global weak and classical solution
zbMATH Keywords: asymptotic behaviour of particles
reviewed by: Mykola Krasnoschok
MaRDI profile type: Publication
full work available at URL: j.jde.2004.05.008
OpenAlex ID: W2126573201
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DOI: 10.1016/J.JDE.2004.05.008
description: scientific article; zbMATH DE number 2117236