Year: 2007
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W1661561905