  We investigate a non-local non linear conservation law, first introduced by
A.C. Fowler to describe morphodynamics of dunes, see \cite{Fow01, Fow02}. A
remarkable feature is the violation of the maximum principle, which allows for
erosion phenomenon. We prove well-posedness for initial data in $L^2$ and give
explicit counterexample for the maximum principle. We also provide numerical
simulations corroborating our theoretical results.
