  In this paper we build models for short-term, mean-term and long-term
dynamics of dune and megariple morphodynamics. They are models that are
degenerated parabolic equations which are, moreover, singularly perturbed. We,
then give an existence and uniqueness result for the short-term and mean-term
models. This result is based on a time-space periodic solution existence result
for degenerated parabolic equation that we set out. Finally the short-term
model is homogenized.
