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December  2008, 1(4): 591-617. doi: 10.3934/krm.2008.1.591

A kinetic model for grain growth

1. 

Hochschulrechenzentrum der Universität Bonn, Wegelerstraße 6, D-53115 Bonn, Germany

2. 

University of Oxford, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom

3. 

Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB

4. 

Instituto de Ciencias Mathemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid, Spain

Received  July 2008 Revised  August 2008 Published  October 2008

We provide a well--posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann--Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self--consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations.

We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super--solutions, a bound from below on the total mass, and a tightness estimate which ensures that no mass is transported to infinity in finite time.
Citation: Reiner Henseler, Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez. A kinetic model for grain growth. Kinetic & Related Models, 2008, 1 (4) : 591-617. doi: 10.3934/krm.2008.1.591
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