The Lifschitz-Slyozov equation with space-diffusion of monomers

Thierry Goudon; Frédéric Lagoutière; Léon M. Tine

doi:10.3934/krm.2012.5.325

Article Contents

2012, Volume 5, Issue 2: 325-355. Doi: 10.3934/krm.2012.5.325

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The Lifschitz-Slyozov equation with space-diffusion of monomers

1.
Project COFFEE, INRIA Sophia Antipolis Méditerranée Research Centre, & Labo. J. A. Dieudonné UMR 7351 CNRS{Université Nice Sophia Antipolis, Parc Valrose, 06108 Nice
2.
Laboratoire de Mathématiques, UMR 8628, CNRS-Université Paris-Sud 11, Bât. 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405 Orsay cedex,
3.
Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d'Ascq cedex

Received: August 31, 2011

Revised: December 31, 2011

Published: May 2012

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Abstract

The Lifschitz--Slyozov system describes the dynamics of mass exchanges between macro--particles and monomers in the theory of coarsening. We consider a variant of the classical model where monomers are subject to space diffusion. We establish the existence--uniqueness of solutions for a wide class of relevant data and kinetic coefficients. We also derive a numerical scheme to simulate the behavior of the solutions.

Keywords:

Lifschitz-Slyozov equation,
theory of coarsening,
PDEs of hybrid type,
existence--uniqueness of solutions,
finite-volume finite-difference schemes.

Mathematics Subject Classification: Primary: 82C21; Secondary: 35G61, 45K05, 82C26.

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