A non-monotone conservation law for dune morphodynamics

Nathaël Alibaud (1) , Pascal Azerad (2) , Damien Isèbe (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: non linear evolution equations; non local operator; maximum principle; integral formula; Fourier transform; pseudo-differential operator

Domaines: Equations aux dérivées partielles [math.AP]

Nathaël Alibaud, Pascal Azerad, Damien Isèbe. A non-monotone conservation law for dune morphodynamics. Differential and integral equations, 2010, 23, pp.155--188. ⟨hal-00173879⟩