It is known that similar physical systems can reveal two quite different ways
of behavior, either coarsening, which creates a uniform state or a large-scale
structure, or formation of ordered or disordered patterns, which are never
homogenized. We present a description of coarsening using simple basic models,
the Allen-Cahn equation and the Cahn-Hilliard equation, and discuss the factors
that may slow down and arrest the process of coarsening. Among them are pinning
of domain walls on inhomogeneities, oscillatory tails of domain walls, nonlocal
interactions, and others. Coarsening of pattern domains is also discussed.Comment: 14 pages. To appear in a Comptes Rendus Physique special issue on
"Coarsening Dynamics", see
https://sites.google.com/site/ppoliti/crp-special-issu
