A non-monotone conservation law for dune morphodynamics

Nathaël Alibaud; Pascal Azerad; Damien Isèbe

hal-00173879, version 1

A non-monotone conservation law for dune morphodynamics

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

Differential and integral equations 23 (2010) 155--188

Abstract: 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.

1: Laboratoire de Mathématiques (LM-Besançon)
CNRS : UMR6623 – Université de Franche-Comté
2: Institut de Mathématiques et de Modélisation de Montpellier (I3M)
CNRS : UMR5149 – Université Montpellier II - Sciences et techniques

Collaboration : ANR projet COPTER NT05-2-42253

hal-00173879, version 1
http://hal.archives-ouvertes.fr/hal-00173879
oai:hal.archives-ouvertes.fr:hal-00173879
From: Pascal Azerad <>
Submitted on: Thursday, 20 September 2007 18:06:26
Updated on: Thursday, 19 November 2009 19:02:07

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