  Wavelength selection in reaction--diffusion systems can be understood as a
coarsening process that is interrupted by counteracting processes at certain
wavelengths. We first show that coarsening in mass-conserving systems is driven
by self-amplifying mass transport between neighboring high-density domains. We
derive a general coarsening criterion and show that coarsening is generically
uninterrupted in two-component systems that conserve mass. The theory is then
generalized to study interrupted coarsening and anti-coarsening due to
weakly-broken mass conservation, providing a general path to analyze wavelength
selection in pattern formation far from equilibrium.
