Universal bounds on coarsening rates for mean-eld models of phase transition
Abstract. We prove one-sided universal bounds on coarsening rates for two kinds of mean-field models of phase transitions, one with a coarsening rate l ∼ t,/2 rate is proved using a new dissipation relation which extends the Kohn–Otto method. In both cases, the dissipation relations are subtle and their proofs are based on a residual lemma,(Lagrange identity) for the Cauchy–Schwarz inequality. Key words. Ostwald ripening, Lifshitz–Slyozov–Wagner equations, scaling exponents AMS subject classifications. 82C26, 35B40, 35Q80, 74N20 DOI. 10.1137/040618047
Published in 2004.