  Dynamics of a one-dimensional growing front with an unstable straight profile
are analyzed. We argue that a coarsening process occurs if and only if the
period \lambda of the steady state solution is an increasing function of its
amplitude A. This statement is rigorously proved for two important classes of
conserved and nonconserved models by investigating the phase diffusion equation
of the steady pattern. We further provide clear numerical evidences for the
growth equation of a stepped crystal surface.
