A non-monotone nonlocal conservation law for dune morphodynamics (Q636884)

The authors study a nonlocal nonlinear conservation law describing morphodynamics of dunes. They prove well-posedness of the problem in \(L^2(\mathbb {R})\), and show that the solutions are regular for positive times. Moreover, they give an explicit counterexample to the maximum principle: they exhibit positive dunes which take negative values in finite time, since the bottom is eroded downstream from the dune. Some numerical results illustrating this fact are also given.