Lectures on Dynamics in Models of Coarsening and Coagulation

Contents 1 Introduction 2 2 A hierarchy of domain coarsening models in one space dimension 5 2.1 Domain walls in the Allen-Cahn equation 5 2.2 Domain wall dynamics by restricted gradient flow 7 2.3 Punctuated equilibrium and 1D bubble bath 11 2.4 Mean-field model of domain growth—the Gallay-Mielke transform 13 2.5 Proof of universal self-similar behavior 19 3 Models of domain coarsening in two and three dimensions 23 3.1 Diffuse and sharp-interface models of nanoscale island coarsening 24 3.2 Gradient structure for Mullins-Sekerka flow 31 3.3 Monopole models by restricted gradient flow of surface energy 33 3.4 Lifshitz-Slyozov-Wagner mean-field model 35 4 Rigorous power-law bounds on coarsening rates—the Kohn-Otto method 40 4.1 Basic inequalities 41 4.2 Bounds on coarsening rates for the LSW mean-field model 43 4.3 Bounds on coarsening rates for the monopole model 44 5 Smoluchowski's coagulation equations 47 5.