A Kinetic Model for Grain Growth

Details A Kinetic Model for Grain Growth A Kinetic Model for Grain Growth

2008-07-22

arxiv.org/abs/0807.3529v1

Kinetic and Related Models, vol 1, no 4, 2008, pp 591 - 617

Mathematics

Analysis of PDEs

24 pages

Scientific paper

10.3934/krm.2008.1.591

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.

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