Résumé
Differential and integral equations 23 (2010) 155--188 We investigate a non-local non linear conservation law, first introduced by A.C. Fowler to describe morphodynamics of dunes, see 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.