## Differential and Integral Equations

### A non-monotone nonlocal conservation law for dune morphodynamics

#### Abstract

We investigate a non-local, non-linear conservation law, first introduced by A.C. Fowler to describe morphodynamics of dunes, see [6, 7]. 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 an explicit counterexample for the maximum principle. We also provide numerical simulations corroborating our theoretical results.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 1/2 (2010), 155-188.

Dates
First available in Project Euclid: 20 December 2012