Séminaire d'Analyse

UPPER BOUNDS FOR COARSENING FOR THE DEGENERATE CAHN-HILLIARD EQUATION
Andrey Shishkov
Thursday 26 November 2009 14:00 -  Tours -  Salle 2290 (Bât E2)

Résumé :
The long time behavior for the degenerate Cahn-Hilliard equation is characterized by the growth of domains in which u(x, t) ≈ u± , where u± denote the “equilibrium phases;” this process is known as coarsening. The degree of coarsening can be quantified in terms of a characteristic length scale, l(t), where l(t) is prescribed via a Liapunov functional and a W^{1, ∞} predual norm of u(x, t). In this paper, we prove upper bounds on l(t) for all temperatures Θ ∈ (0, Θc ), where Θc denotes the “critical temperature,” and for arbitrary mean concentrations, u ∈ (u− , u+ ). Our results generalize the upper bounds obtained by Kohn & Otto [14]. In particular, we demonstrate that transitions may take place in the nature of the coarsening bounds during the coarsening process.

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