A kinetic model for grain growth [Elektronische Ressource] / von Reiner Henseler

A kinetic model for grain growthDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIder Humboldt-Universität zu BerlinvonReiner Thorsten Henselergeboren am 21. Dezember 1977 in BonnPräsident der Humboldt-Universität zu Berlin:Prof. Dr. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Wolfgang CoyGutachter:1. Prof. Dr. Barbara Niethammer2. Prof. Dr. Juan J. L. Velázquez3. Priv.-Doz. Dr. Lutz ReckeTag der Verteidigung: 17. September 2007AbstractThe subject matter of this thesis is a detailed analysis of the self–consistentkinetic model for grain growth introduced by Fradkov [5]. The model isbased on the von Neumann–Mullins law describing the change of area ofgrainsaccordingtotheirtopologicalclass, i.e. thenumberofedgestheyhave.Topological events are performed by coupling terms between equations forthe number densities of different topological classes. The resulting systemof transport equations is infinite–dimensional with a tridiagonal couplingstructure. Self–consistency of this kinetic model is achieved by introducinga coupling’s weight Γ making the equations nonlinear and nonlocal in space.We start with an introduction in the first chapter. Afterwards in the sec-ond chapter we derive Fradkov’s model and carry out formal calculations toillustrate self–consistency.