Global-in-time existence of perturbations around travelling-waves

Afaf Bouharguane (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: nonlinear and nonlocal conservation law; fractional anti-diffusive operator; Duhamel formulation; travelling-wave; global-in-time existence; global-in-time existence.

Domaines: Equations aux dérivées partielles [math.AP]

Afaf Bouharguane. Global-in-time existence of perturbations around travelling-waves. 2011. ⟨hal-00605134⟩