A kinetic model for grain growth
نویسندگان
چکیده
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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