Global well-posedness and instability of travelling-waves for a nonlocal conservation law

Afaf Bouharguane (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler. We begin by proving the global-in-time well-posedness in the neighbourhood of travelling-waves. We next show the instability of travelling-waves solutions of the Fowler equation.

Mots clés: nonlocal evolution equation; fractional anti-diffusive operator; Duhamel formulation; travelling-wave; instability.; instability

Domaines: Equations aux dérivées partielles [math.AP]

Afaf Bouharguane. Global well-posedness and instability of travelling-waves for a nonlocal conservation law. 2010. ⟨hal-00529766v1⟩