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International Journal of Differential Equations
Volume 2011, Article ID 408704, 24 pages
http://dx.doi.org/10.1155/2011/408704
Research Article

Global Existence of Solutions to the Fowler Equation in a Neighbourhood of Travelling-Waves

Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 CNRS, Université Montpellier 2, Place Eugène Bataillon, CC 051, 34095 Montpellier, France

Received 30 June 2011; Accepted 27 August 2011

Academic Editor: Khalil Ezzinbi

Copyright © 2011 Afaf Bouharguane. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-in-time well-posedness in the neighbourhood of travelling-waves solutions of the Fowler equation.